Theorem vtocld

Description: Implicit substitution of a class for a setvar variable. (Contributed by Mario Carneiro, 15-Oct-2016)

	Ref	Expression
Hypotheses	vtocld.1	|- ( ph -> A e. V )
	vtocld.2	|- ( ( ph /\ x = A ) -> ( ps <-> ch ) )
	vtocld.3	|- ( ph -> ps )
Assertion	vtocld	|- ( ph -> ch )

Proof

Step	Hyp	Ref	Expression
1		vtocld.1	|- ( ph -> A e. V )
2		vtocld.2	|- ( ( ph /\ x = A ) -> ( ps <-> ch ) )
3		vtocld.3	|- ( ph -> ps )
4		nfv	|- F/ x ph
5		nfcvd	|- ( ph -> F/_ x A )
6		nfvd	|- ( ph -> F/ x ch )
7	1 2 3 4 5 6	vtocldf	|- ( ph -> ch )