Theorem rabbidvaOLD

Description: Obsolete proof of rabbidva as of 4-Dec-2023. (Contributed by NM, 28-Nov-2003) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	rabbidva.1	|- ( ( ph /\ x e. A ) -> ( ps <-> ch ) )
Assertion	rabbidvaOLD	|- ( ph -> { x e. A | ps } = { x e. A | ch } )

Proof

Step	Hyp	Ref	Expression
1		rabbidva.1	|- ( ( ph /\ x e. A ) -> ( ps <-> ch ) )
2	1	ralrimiva	|- ( ph -> A. x e. A ( ps <-> ch ) )
3		rabbi	|- ( A. x e. A ( ps <-> ch ) <-> { x e. A | ps } = { x e. A | ch } )
4	2 3	sylib	|- ( ph -> { x e. A | ps } = { x e. A | ch } )