Theorem sbciedOLD

Description: Obsolete version of sbcied as of 12-Oct-2024. (Contributed by NM, 13-Dec-2014) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	sbciedOLD.1	|- ( ph -> A e. V )
	sbciedOLD.2	|- ( ( ph /\ x = A ) -> ( ps <-> ch ) )
Assertion	sbciedOLD	|- ( ph -> ( [. A / x ]. ps <-> ch ) )

Proof

Step	Hyp	Ref	Expression
1		sbciedOLD.1	|- ( ph -> A e. V )
2		sbciedOLD.2	|- ( ( ph /\ x = A ) -> ( ps <-> ch ) )
3		nfv	|- F/ x ph
4		nfvd	|- ( ph -> F/ x ch )
5	1 2 3 4	sbciedf	|- ( ph -> ( [. A / x ]. ps <-> ch ) )