Theorem vtoclb

Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 23-Dec-1993)

	Ref	Expression
Hypotheses	vtoclb.1	|- A e. _V
	vtoclb.2	|- ( x = A -> ( ph <-> ch ) )
	vtoclb.3	|- ( x = A -> ( ps <-> th ) )
	vtoclb.4	|- ( ph <-> ps )
Assertion	vtoclb	|- ( ch <-> th )

Proof

Step	Hyp	Ref	Expression
1		vtoclb.1	|- A e. _V
2		vtoclb.2	|- ( x = A -> ( ph <-> ch ) )
3		vtoclb.3	|- ( x = A -> ( ps <-> th ) )
4		vtoclb.4	|- ( ph <-> ps )
5	2 3	bibi12d	|- ( x = A -> ( ( ph <-> ps ) <-> ( ch <-> th ) ) )
6	1 5 4	vtocl	|- ( ch <-> th )