bnj581

Description: Technical lemma for bnj580 . 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) Remove unnecessary distinct variable conditions. (Revised by Andrew Salmon, 9-Jul-2011) (New usage is discouraged.)

	Ref	Expression
Hypotheses	bnj581.3	$⊢ χ \leftrightarrow (f Fn n \land φ \land ψ)$
	bnj581.4	No typesetting found for \|- ( ph' <-> [. g / f ]. ph ) with typecode \|-
	bnj581.5	No typesetting found for \|- ( ps' <-> [. g / f ]. ps ) with typecode \|-
	bnj581.6	No typesetting found for \|- ( ch' <-> [. g / f ]. ch ) with typecode \|-
Assertion	bnj581	Could not format assertion : No typesetting found for \|- ( ch' <-> ( g Fn n /\ ph' /\ ps' ) ) with typecode \|-

Proof

Step	Hyp	Ref	Expression
1		bnj581.3	$⊢ χ \leftrightarrow (f Fn n \land φ \land ψ)$
2		bnj581.4	Could not format ( ph' <-> [. g / f ]. ph ) : No typesetting found for \|- ( ph' <-> [. g / f ]. ph ) with typecode \|-
3		bnj581.5	Could not format ( ps' <-> [. g / f ]. ps ) : No typesetting found for \|- ( ps' <-> [. g / f ]. ps ) with typecode \|-
4		bnj581.6	Could not format ( ch' <-> [. g / f ]. ch ) : No typesetting found for \|- ( ch' <-> [. g / f ]. ch ) with typecode \|-
5	1	sbcbii	$⊢ \underset{˙}{[} g / f \underset{˙}{]} χ \leftrightarrow \underset{˙}{[} g / f \underset{˙}{]} (f Fn n \land φ \land ψ)$
6		sbc3an	$⊢ \underset{˙}{[} g / f \underset{˙}{]} (f Fn n \land φ \land ψ) \leftrightarrow (\underset{˙}{[} g / f \underset{˙}{]} f Fn n \land \underset{˙}{[} g / f \underset{˙}{]} φ \land \underset{˙}{[} g / f \underset{˙}{]} ψ)$
7		bnj62	$⊢ \underset{˙}{[} g / f \underset{˙}{]} f Fn n \leftrightarrow g Fn n$
8	7	bicomi	$⊢ g Fn n \leftrightarrow \underset{˙}{[} g / f \underset{˙}{]} f Fn n$
9	8 2 3	3anbi123i	Could not format ( ( g Fn n /\ ph' /\ ps' ) <-> ( [. g / f ]. f Fn n /\ [. g / f ]. ph /\ [. g / f ]. ps ) ) : No typesetting found for \|- ( ( g Fn n /\ ph' /\ ps' ) <-> ( [. g / f ]. f Fn n /\ [. g / f ]. ph /\ [. g / f ]. ps ) ) with typecode \|-
10	6 9	bitr4i	Could not format ( [. g / f ]. ( f Fn n /\ ph /\ ps ) <-> ( g Fn n /\ ph' /\ ps' ) ) : No typesetting found for \|- ( [. g / f ]. ( f Fn n /\ ph /\ ps ) <-> ( g Fn n /\ ph' /\ ps' ) ) with typecode \|-
11	4 5 10	3bitri	Could not format ( ch' <-> ( g Fn n /\ ph' /\ ps' ) ) : No typesetting found for \|- ( ch' <-> ( g Fn n /\ ph' /\ ps' ) ) with typecode \|-

Metamath Proof Explorer

Theorem bnj581

Proof