Theorem anabs7 852

Description: Absorption into embedded conjunct. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 17-Nov-2013.)

Assertion

Ref	Expression
anabs7	|- ( ( ps /\ ( ph /\ ps ) ) <-> ( ph /\ ps ) )

Proof of Theorem anabs7

Step	Hyp	Ref	Expression
1		simpr 477	. . 3 |- ( ( ph /\ ps ) -> ps )
2	1	pm4.71ri 665	. 2 |- ( ( ph /\ ps ) <-> ( ps /\ ( ph /\ ps ) ) )
3	2	bicomi 214	1 |- ( ( ps /\ ( ph /\ ps ) ) <-> ( ph /\ ps ) )

Syntax hints:   <-> wb 196   /\ 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:  prtlem15  34160  un2122  39017