Theorem sbcied

Description: Conversion of implicit substitution to explicit class substitution, deduction form. (Contributed by NM, 13-Dec-2014)

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

Proof

Step	Hyp	Ref	Expression
1		sbcied.1	|- ( ph -> A e. V )
2		sbcied.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 ) )