Theorem bnj589

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
Hypothesis	bnj589.1	|- ( ps <-> A. i e. _om ( suc i e. n -> ( f ` suc i ) = U_ y e. ( f ` i ) _pred ( y , A , R ) ) )
Assertion	bnj589	|- ( ps <-> A. k e. _om ( suc k e. n -> ( f ` suc k ) = U_ y e. ( f ` k ) _pred ( y , A , R ) ) )

Proof

Step	Hyp	Ref	Expression
1		bnj589.1	|- ( ps <-> A. i e. _om ( suc i e. n -> ( f ` suc i ) = U_ y e. ( f ` i ) _pred ( y , A , R ) ) )
2	1	bnj222	|- ( ps <-> A. k e. _om ( suc k e. n -> ( f ` suc k ) = U_ y e. ( f ` k ) _pred ( y , A , R ) ) )