Theorem anabs1 503

Description: Absorption into embedded conjunct.

Assertion

Ref	Expression
anabs1	|- (((ph /\ ps) /\ ph) <-> (ph /\ ps))

Proof of Theorem anabs1

Step	Hyp	Ref	Expression
1		pm3.26 326	. 2 |- (((ph /\ ps) /\ ph) -> (ph /\ ps))
2		pm3.26 326	. . 3 |- ((ph /\ ps) -> ph)
3	2	ancli 303	. 2 |- ((ph /\ ps) -> ((ph /\ ps) /\ ph))
4	1, 3	impbii 164	1 |- (((ph /\ ps) /\ ph) <-> (ph /\ ps))

Syntax hints:   <-> wb 153   /\ wa 230

This theorem is referenced by:  anabs5 504  euan 1470  poirr 2901

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 154  df-an 232

Copyright terms: Public domain