Theorem anabs5 851

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 525	. . 3 |- ( ph -> ( ps <-> ( ph /\ ps ) ) )
2	1	bicomd 213	. 2 |- ( ph -> ( ( ph /\ ps ) <-> ps ) )
3	2	pm5.32i 669	1 |- ( ( ph /\ ( 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:  axrep5  4776  axsep2  4782  bj-axrep5  32792  elinintrab  37883  2sb5nd  38776  eelTT1  38935  uun121  39010  uunTT1  39020  uunTT1p1  39021  uunTT1p2  39022  uun111  39032  uun2221  39040  uun2221p1  39041  uun2221p2  39042  2sb5ndVD  39146  2sb5ndALT  39168