Theorem sbc2ieOLD

Description: Obsolete version of sbc2ie as of 12-Oct-2024. (Contributed by NM, 16-Dec-2008) (Revised by Mario Carneiro, 19-Dec-2013) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	sbc2ieOLD.1	|- A e. _V
	sbc2ieOLD.2	|- B e. _V
	sbc2ieOLD.3	|- ( ( x = A /\ y = B ) -> ( ph <-> ps ) )
Assertion	sbc2ieOLD	|- ( [. A / x ]. [. B / y ]. ph <-> ps )

Proof

Step	Hyp	Ref	Expression
1		sbc2ieOLD.1	|- A e. _V
2		sbc2ieOLD.2	|- B e. _V
3		sbc2ieOLD.3	|- ( ( x = A /\ y = B ) -> ( ph <-> ps ) )
4		nfv	|- F/ x ps
5		nfv	|- F/ y ps
6	2	nfth	|- F/ x B e. _V
7	4 5 6 3	sbc2iegf	|- ( ( A e. _V /\ B e. _V ) -> ( [. A / x ]. [. B / y ]. ph <-> ps ) )
8	1 2 7	mp2an	|- ( [. A / x ]. [. B / y ]. ph <-> ps )