bnj1039

Description: Technical lemma for bnj69 . 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	bnj1039.1	$⊢ ψ \leftrightarrow \forall i \in ω (suc i \in n \to f (suc i) = ⋃_{y \in f (i)} pred (y, A, R))$
	bnj1039.2	No typesetting found for \|- ( ps' <-> [. j / i ]. ps ) with typecode \|-
Assertion	bnj1039	Could not format assertion : No typesetting found for \|- ( ps' <-> A. i e. _om ( suc i e. n -> ( f ` suc i ) = U_ y e. ( f ` i ) _pred ( y , A , R ) ) ) with typecode \|-

Proof

Step	Hyp	Ref	Expression
1		bnj1039.1	$⊢ ψ \leftrightarrow \forall i \in ω (suc i \in n \to f (suc i) = ⋃_{y \in f (i)} pred (y, A, R))$
2		bnj1039.2	Could not format ( ps' <-> [. j / i ]. ps ) : No typesetting found for \|- ( ps' <-> [. j / i ]. ps ) with typecode \|-
3		vex	$⊢ j \in V$
4		nfra1	$⊢ Ⅎ i \forall i \in ω (suc i \in n \to f (suc i) = ⋃_{y \in f (i)} pred (y, A, R))$
5	1 4	nfxfr	$⊢ Ⅎ i ψ$
6	3 5	sbcgfi	$⊢ \underset{˙}{[} j / i \underset{˙}{]} ψ \leftrightarrow ψ$
7	2 6 1	3bitri	Could not format ( ps' <-> A. i e. _om ( suc i e. n -> ( f ` suc i ) = U_ y e. ( f ` i ) _pred ( y , A , R ) ) ) : No typesetting found for \|- ( ps' <-> A. i e. _om ( suc i e. n -> ( f ` suc i ) = U_ y e. ( f ` i ) _pred ( y , A , R ) ) ) with typecode \|-

Metamath Proof Explorer

Theorem bnj1039

Proof