Theorem csbiegf

Description: Conversion of implicit substitution to explicit substitution into a class. (Contributed by NM, 11-Nov-2005) (Revised by Mario Carneiro, 13-Oct-2016)

	Ref	Expression
Hypotheses	csbiegf.1	|- ( A e. V -> F/_ x C )
	csbiegf.2	|- ( x = A -> B = C )
Assertion	csbiegf	|- ( A e. V -> [_ A / x ]_ B = C )

Proof

Step	Hyp	Ref	Expression
1		csbiegf.1	|- ( A e. V -> F/_ x C )
2		csbiegf.2	|- ( x = A -> B = C )
3	2	ax-gen	|- A. x ( x = A -> B = C )
4		csbiebt	|- ( ( A e. V /\ F/_ x C ) -> ( A. x ( x = A -> B = C ) <-> [_ A / x ]_ B = C ) )
5	1 4	mpdan	|- ( A e. V -> ( A. x ( x = A -> B = C ) <-> [_ A / x ]_ B = C ) )
6	3 5	mpbii	|- ( A e. V -> [_ A / x ]_ B = C )