Theorem anabs1 494

Description: Absorption into embedded conjunct.

Assertion

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

Proof of Theorem anabs1

Step	Hyp	Ref	Expression
1		pm3.26 319	. 2 |- (((ph /\ ps) /\ ph) -> (ph /\ ps))
2		pm3.26 319	. . 3 |- ((ph /\ ps) -> ph)
3	2	ancli 296	. 2 |- ((ph /\ ps) -> ((ph /\ ps) /\ ph))
4	1, 3	impbi 157	1 |- (((ph /\ ps) /\ ph) <-> (ph /\ ps))

Syntax hints:   <-> wb 146   /\ wa 223

This theorem is referenced by:  anabs5 495  euan 1430  poirr 2851

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 147  df-an 225

Copyright terms: Public domain