Theorem sbcie

Description: Conversion of implicit substitution to explicit class substitution. (Contributed by NM, 4-Sep-2004)

	Ref	Expression
Hypotheses	sbcie.1	|- A e. _V
	sbcie.2	|- ( x = A -> ( ph <-> ps ) )
Assertion	sbcie	|- ( [. A / x ]. ph <-> ps )

Proof

Step	Hyp	Ref	Expression
1		sbcie.1	|- A e. _V
2		sbcie.2	|- ( x = A -> ( ph <-> ps ) )
3	2	sbcieg	|- ( A e. _V -> ( [. A / x ]. ph <-> ps ) )
4	1 3	ax-mp	|- ( [. A / x ]. ph <-> ps )