Theorem ggen31

Description: gen31 without virtual deductions. (Contributed by Alan Sare, 22-Jul-2012) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	ggen31.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
Assertion	ggen31	|- ( ph -> ( ps -> ( ch -> A. x th ) ) )

Proof

Step	Hyp	Ref	Expression
1		ggen31.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
2	1	imp	|- ( ( ph /\ ps ) -> ( ch -> th ) )
3	2	alrimdv	|- ( ( ph /\ ps ) -> ( ch -> A. x th ) )
4	3	ex	|- ( ph -> ( ps -> ( ch -> A. x th ) ) )