Theorem ggen31 38760

Description: gen31 38846 without virtual deductions. (Contributed by Alan Sare, 22-Jul-2012.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
ggen31.1	|- ( ph -> ( ps -> ( ch -> th ) ) )

Assertion

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

Distinct variable groups:   ch, x   ph, x   ps, x

Allowed substitution hint:   th( x)

Proof of Theorem ggen31

Step	Hyp	Ref	Expression
1		ggen31.1	. . . 4 |- ( ph -> ( ps -> ( ch -> th ) ) )
2	1	imp 445	. . 3 |- ( ( ph /\ ps ) -> ( ch -> th ) )
3	2	alrimdv 1857	. 2 |- ( ( ph /\ ps ) -> ( ch -> A. x th ) )
4	3	ex 450	1 |- ( ph -> ( ps -> ( ch -> A. x th ) ) )

Syntax hints:   -> wi 4   /\ wa 384   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839

This theorem depends on definitions:  df-bi 197  df-an 386

This theorem is referenced by:  onfrALTlem2  38761  gen31  38846