Theorem csbied

Description: Conversion of implicit substitution to explicit substitution into a class. (Contributed by Mario Carneiro, 2-Dec-2014) (Revised by Mario Carneiro, 13-Oct-2016)

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

Proof

Step	Hyp	Ref	Expression
1		csbied.1	|- ( ph -> A e. V )
2		csbied.2	|- ( ( ph /\ x = A ) -> B = C )
3		nfv	|- F/ x ph
4		nfcvd	|- ( ph -> F/_ x C )
5	3 4 1 2	csbiedf	|- ( ph -> [_ A / x ]_ B = C )