Theorem 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	$$⊢\psi \leftrightarrow \forall i\in \mathrm{\omega }\left(\mathrm{suc}i\in N\to f\left(\mathrm{suc}i\right)=\bigcup _{y\in f\left(i\right)}pred\left(y,A,R\right)\right)$$
	bnj965.2	No typesetting found for |- ( ps" <-> [. G / f ]. ps ) with typecode |-
	bnj965.12000	$$⊢C=\bigcup _{y\in f\left(m\right)}pred\left(y,A,R\right)$$
	bnj965.13000	$$⊢G=f\cup \left\{⟨n,C⟩\right\}$$
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	$$⊢\psi \leftrightarrow \forall i\in \mathrm{\omega }\left(\mathrm{suc}i\in N\to f\left(\mathrm{suc}i\right)=\bigcup _{y\in f\left(i\right)}pred\left(y,A,R\right)\right)$$
2		bnj965.2	Could not format ( ps" <-> [. G / f ]. ps ) : No typesetting found for |- ( ps" <-> [. G / f ]. ps ) with typecode |-
3		bnj965.12000	$$⊢C=\bigcup _{y\in f\left(m\right)}pred\left(y,A,R\right)$$
4		bnj965.13000	$$⊢G=f\cup \left\{⟨n,C⟩\right\}$$
5	4	bnj918	$$⊢G\in \mathrm{V}$$
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 |-