Theorem anim12d1 587

Description: Variant of anim12d 586 where the second implication does not depend on the antecedent. (Contributed by Rodolfo Medina, 12-Oct-2010.)

Hypotheses

Ref	Expression
anim12d1.1	|- ( ph -> ( ps -> ch ) )
anim12d1.2	|- ( th -> ta )

Assertion

Ref	Expression
anim12d1	|- ( ph -> ( ( ps /\ th ) -> ( ch /\ ta ) ) )

Proof of Theorem anim12d1

Step	Hyp	Ref	Expression
1		anim12d1.1	. 2 |- ( ph -> ( ps -> ch ) )
2		anim12d1.2	. . 3 |- ( th -> ta )
3	2	a1i 11	. 2 |- ( ph -> ( th -> ta ) )
4	1, 3	anim12d 586	1 |- ( ph -> ( ( ps /\ th ) -> ( ch /\ ta ) ) )

Syntax hints:   -> wi 4   /\ wa 384

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

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

This theorem is referenced by:  upgrwlkdvdelem  26632