Theorem csbied2

Description: Conversion of implicit substitution to explicit class substitution, deduction form. (Contributed by Mario Carneiro, 2-Jan-2017)

	Ref	Expression
Hypotheses	csbied2.1	|- ( ph -> A e. V )
	csbied2.2	|- ( ph -> A = B )
	csbied2.3	|- ( ( ph /\ x = B ) -> C = D )
Assertion	csbied2	|- ( ph -> [_ A / x ]_ C = D )

Proof

Step	Hyp	Ref	Expression
1		csbied2.1	|- ( ph -> A e. V )
2		csbied2.2	|- ( ph -> A = B )
3		csbied2.3	|- ( ( ph /\ x = B ) -> C = D )
4		id	|- ( x = A -> x = A )
5	4 2	sylan9eqr	|- ( ( ph /\ x = A ) -> x = B )
6	5 3	syldan	|- ( ( ph /\ x = A ) -> C = D )
7	1 6	csbied	|- ( ph -> [_ A / x ]_ C = D )