Theorem 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	$$⊢\psi \leftrightarrow \forall i\in \mathrm{\omega }\left(\mathrm{suc}i\in n\to f\left(\mathrm{suc}i\right)=\bigcup _{y\in f\left(i\right)}pred\left(y,A,R\right)\right)$$
	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	$$⊢\psi \leftrightarrow \forall i\in \mathrm{\omega }\left(\mathrm{suc}i\in n\to f\left(\mathrm{suc}i\right)=\bigcup _{y\in f\left(i\right)}pred\left(y,A,R\right)\right)$$
2		bnj1039.2	Could not format ( ps' <-> [. j / i ]. ps ) : No typesetting found for |- ( ps' <-> [. j / i ]. ps ) with typecode |-
3		vex	$$⊢j\in \mathrm{V}$$
4		nfra1	$$⊢Ⅎi\forall i\in \mathrm{\omega }\left(\mathrm{suc}i\in n\to f\left(\mathrm{suc}i\right)=\bigcup _{y\in f\left(i\right)}pred\left(y,A,R\right)\right)$$
5	1 4	nfxfr	$$⊢Ⅎi\psi$$
6	3 5	sbcgfi	$$⊢\underset{\dot{}}{[}j/i\underset{\dot{}}{]}\psi \leftrightarrow \psi$$
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 |-