Theorem anabs7 494

Description: Absorption into embedded conjunct.

Assertion

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

Proof of Theorem anabs7

Step	Hyp	Ref	Expression
1		pm3.27 323	. 2 |- ((ps /\ (ph /\ ps)) -> (ph /\ ps))
2		pm3.27 323	. . 3 |- ((ph /\ ps) -> ps)
3	2	ancri 297	. 2 |- ((ph /\ ps) -> (ps /\ (ph /\ ps)))
4	1, 3	impbi 157	1 |- ((ps /\ (ph /\ ps)) <-> (ph /\ ps))

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

This theorem is referenced by:  suppsr3 5224

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