Theorem anabs5 573

Description: Absorption into embedded conjunct. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 9-Dec-2012.)

Assertion

Ref	Expression
anabs5	|- ( ( ph /\ ( ph /\ ps ) ) <-> ( ph /\ ps ) )

Proof of Theorem anabs5

Step	Hyp	Ref	Expression
1		ibar 301	. . 3 |- ( ph -> ( ps <-> ( ph /\ ps ) ) )
2	1	bicomd 141	. 2 |- ( ph -> ( ( ph /\ ps ) <-> ps ) )
3	2	pm5.32i 454	1 |- ( ( ph /\ ( ph /\ ps ) ) <-> ( ph /\ ps ) )

Syntax hints:   /\ wa 104   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  mo3h  2098  indif  3406  axsep2  4152