Theorem an3 868

Description: A rearrangement of conjuncts. (Contributed by Rodolfo Medina, 25-Sep-2010.)

Assertion

Ref	Expression
an3	|- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) -> ( ph /\ th ) )

Proof of Theorem an3

Step	Hyp	Ref	Expression
1		an43 867	. 2 |- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ph /\ th ) /\ ( ps /\ ch ) ) )
2	1	simplbi 476	1 |- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) -> ( ph /\ th ) )

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:  catideu  16336  prtlem15  34160  clsk1indlem3  38341