bnj965

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	bnj965.1	$⊢ ψ \leftrightarrow \forall i \in ω (suc i \in N \to f (suc i) = ⋃_{y \in f (i)} pred (y, A, R))$
	bnj965.2	No typesetting found for \|- ( ps" <-> [. G / f ]. ps ) with typecode \|-
	bnj965.12000	$⊢ C = ⋃_{y \in f (m)} pred (y, A, R)$
	bnj965.13000	$⊢ G = f \cup \{⟨n, C⟩\}$
Assertion	bnj965	Could not format assertion : No typesetting found for \|- ( ps" <-> A. i e. _om ( suc i e. N -> ( G ` suc i ) = U_ y e. ( G ` i ) _pred ( y , A , R ) ) ) with typecode \|-

Proof

Step	Hyp	Ref	Expression
1		bnj965.1	$⊢ ψ \leftrightarrow \forall i \in ω (suc i \in N \to f (suc i) = ⋃_{y \in f (i)} pred (y, A, R))$
2		bnj965.2	Could not format ( ps" <-> [. G / f ]. ps ) : No typesetting found for \|- ( ps" <-> [. G / f ]. ps ) with typecode \|-
3		bnj965.12000	$⊢ C = ⋃_{y \in f (m)} pred (y, A, R)$
4		bnj965.13000	$⊢ G = f \cup \{⟨n, C⟩\}$
5	4	bnj918	$⊢ G \in V$
6	1 2 5 3 4	bnj1000	Could not format ( ps" <-> A. i e. _om ( suc i e. N -> ( G ` suc i ) = U_ y e. ( G ` i ) _pred ( y , A , R ) ) ) : No typesetting found for \|- ( ps" <-> A. i e. _om ( suc i e. N -> ( G ` suc i ) = U_ y e. ( G ` i ) _pred ( y , A , R ) ) ) with typecode \|-

Metamath Proof Explorer

Theorem bnj965

Proof