bnj207

Description: Technical lemma for bnj852 . This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypotheses	bnj207.1	$⊢ χ \leftrightarrow ((R FrSe A \land x \in A) \to \exists! f (f Fn n \land φ \land ψ))$
	bnj207.2	No typesetting found for \|- ( ph' <-> [. M / n ]. ph ) with typecode \|-
	bnj207.3	No typesetting found for \|- ( ps' <-> [. M / n ]. ps ) with typecode \|-
	bnj207.4	No typesetting found for \|- ( ch' <-> [. M / n ]. ch ) with typecode \|-
	bnj207.5	$⊢ M \in V$
Assertion	bnj207	Could not format assertion : No typesetting found for \|- ( ch' <-> ( ( R _FrSe A /\ x e. A ) -> E! f ( f Fn M /\ ph' /\ ps' ) ) ) with typecode \|-

Proof

Step	Hyp	Ref	Expression
1		bnj207.1	$⊢ χ \leftrightarrow ((R FrSe A \land x \in A) \to \exists! f (f Fn n \land φ \land ψ))$
2		bnj207.2	Could not format ( ph' <-> [. M / n ]. ph ) : No typesetting found for \|- ( ph' <-> [. M / n ]. ph ) with typecode \|-
3		bnj207.3	Could not format ( ps' <-> [. M / n ]. ps ) : No typesetting found for \|- ( ps' <-> [. M / n ]. ps ) with typecode \|-
4		bnj207.4	Could not format ( ch' <-> [. M / n ]. ch ) : No typesetting found for \|- ( ch' <-> [. M / n ]. ch ) with typecode \|-
5		bnj207.5	$⊢ M \in V$
6	1	sbcbii	$⊢ \underset{˙}{[} M / n \underset{˙}{]} χ \leftrightarrow \underset{˙}{[} M / n \underset{˙}{]} ((R FrSe A \land x \in A) \to \exists! f (f Fn n \land φ \land ψ))$
7		nfv	$⊢ Ⅎ n (R FrSe A \land x \in A)$
8	7	sbc19.21g	$⊢ M \in V \to (\underset{˙}{[} M / n \underset{˙}{]} ((R FrSe A \land x \in A) \to \exists! f (f Fn n \land φ \land ψ)) \leftrightarrow ((R FrSe A \land x \in A) \to \underset{˙}{[} M / n \underset{˙}{]} \exists! f (f Fn n \land φ \land ψ)))$
9	5 8	ax-mp	$⊢ \underset{˙}{[} M / n \underset{˙}{]} ((R FrSe A \land x \in A) \to \exists! f (f Fn n \land φ \land ψ)) \leftrightarrow ((R FrSe A \land x \in A) \to \underset{˙}{[} M / n \underset{˙}{]} \exists! f (f Fn n \land φ \land ψ))$
10	5	bnj89	$⊢ \underset{˙}{[} M / n \underset{˙}{]} \exists! f (f Fn n \land φ \land ψ) \leftrightarrow \exists! f \underset{˙}{[} M / n \underset{˙}{]} (f Fn n \land φ \land ψ)$
11	5	bnj90	$⊢ \underset{˙}{[} M / n \underset{˙}{]} f Fn n \leftrightarrow f Fn M$
12	11	bicomi	$⊢ f Fn M \leftrightarrow \underset{˙}{[} M / n \underset{˙}{]} f Fn n$
13	12 2 3 5	bnj206	Could not format ( [. M / n ]. ( f Fn n /\ ph /\ ps ) <-> ( f Fn M /\ ph' /\ ps' ) ) : No typesetting found for \|- ( [. M / n ]. ( f Fn n /\ ph /\ ps ) <-> ( f Fn M /\ ph' /\ ps' ) ) with typecode \|-
14	13	eubii	Could not format ( E! f [. M / n ]. ( f Fn n /\ ph /\ ps ) <-> E! f ( f Fn M /\ ph' /\ ps' ) ) : No typesetting found for \|- ( E! f [. M / n ]. ( f Fn n /\ ph /\ ps ) <-> E! f ( f Fn M /\ ph' /\ ps' ) ) with typecode \|-
15	10 14	bitri	Could not format ( [. M / n ]. E! f ( f Fn n /\ ph /\ ps ) <-> E! f ( f Fn M /\ ph' /\ ps' ) ) : No typesetting found for \|- ( [. M / n ]. E! f ( f Fn n /\ ph /\ ps ) <-> E! f ( f Fn M /\ ph' /\ ps' ) ) with typecode \|-
16	15	imbi2i	Could not format ( ( ( R _FrSe A /\ x e. A ) -> [. M / n ]. E! f ( f Fn n /\ ph /\ ps ) ) <-> ( ( R _FrSe A /\ x e. A ) -> E! f ( f Fn M /\ ph' /\ ps' ) ) ) : No typesetting found for \|- ( ( ( R _FrSe A /\ x e. A ) -> [. M / n ]. E! f ( f Fn n /\ ph /\ ps ) ) <-> ( ( R _FrSe A /\ x e. A ) -> E! f ( f Fn M /\ ph' /\ ps' ) ) ) with typecode \|-
17	9 16	bitri	Could not format ( [. M / n ]. ( ( R _FrSe A /\ x e. A ) -> E! f ( f Fn n /\ ph /\ ps ) ) <-> ( ( R _FrSe A /\ x e. A ) -> E! f ( f Fn M /\ ph' /\ ps' ) ) ) : No typesetting found for \|- ( [. M / n ]. ( ( R _FrSe A /\ x e. A ) -> E! f ( f Fn n /\ ph /\ ps ) ) <-> ( ( R _FrSe A /\ x e. A ) -> E! f ( f Fn M /\ ph' /\ ps' ) ) ) with typecode \|-
18	6 17	bitri	Could not format ( [. M / n ]. ch <-> ( ( R _FrSe A /\ x e. A ) -> E! f ( f Fn M /\ ph' /\ ps' ) ) ) : No typesetting found for \|- ( [. M / n ]. ch <-> ( ( R _FrSe A /\ x e. A ) -> E! f ( f Fn M /\ ph' /\ ps' ) ) ) with typecode \|-
19	4 18	bitri	Could not format ( ch' <-> ( ( R _FrSe A /\ x e. A ) -> E! f ( f Fn M /\ ph' /\ ps' ) ) ) : No typesetting found for \|- ( ch' <-> ( ( R _FrSe A /\ x e. A ) -> E! f ( f Fn M /\ ph' /\ ps' ) ) ) with typecode \|-

Metamath Proof Explorer

Theorem bnj207

Proof