Theorem ralrexbidOLD

Description: Obsolete version of ralrexbid as of 13-Nov-2023. (Contributed by AV, 21-Oct-2023) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	ralrexbid.1	|- ( ph -> ( ps <-> th ) )
Assertion	ralrexbidOLD	|- ( A. x e. A ph -> ( E. x e. A ps <-> E. x e. A th ) )

Proof

Step	Hyp	Ref	Expression
1		ralrexbid.1	|- ( ph -> ( ps <-> th ) )
2		nfra1	|- F/ x A. x e. A ph
3		rspa	|- ( ( A. x e. A ph /\ x e. A ) -> ph )
4	3 1	syl	|- ( ( A. x e. A ph /\ x e. A ) -> ( ps <-> th ) )
5	2 4	rexbida	|- ( A. x e. A ph -> ( E. x e. A ps <-> E. x e. A th ) )