Theorem vtoclbg

Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 29-Apr-1994)

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

Proof

Step	Hyp	Ref	Expression
1		vtoclbg.1	|- ( x = A -> ( ph <-> ch ) )
2		vtoclbg.2	|- ( x = A -> ( ps <-> th ) )
3		vtoclbg.3	|- ( ph <-> ps )
4	1 2	bibi12d	|- ( x = A -> ( ( ph <-> ps ) <-> ( ch <-> th ) ) )
5	4 3	vtoclg	|- ( A e. V -> ( ch <-> th ) )