Theorem anabss3 502

Description: Absorption of antecedent into conjunction.

Hypothesis

Ref	Expression
anabss3.1	|- (((ph /\ ps) /\ ps) -> ch)

Assertion

Ref	Expression
anabss3	|- ((ph /\ ps) -> ch)

Proof of Theorem anabss3

Step	Hyp	Ref	Expression
1		anabss3.1	. . 3 |- (((ph /\ ps) /\ ps) -> ch)
2	1	adantrl 396	. 2 |- (((ph /\ ps) /\ (ph /\ ps)) -> ch)
3	2	anidms 436	1 |- ((ph /\ ps) -> ch)

Syntax hints:   -> wi 3   /\ wa 223

This theorem is referenced by:  anabsan2 507  mapenlem1 4495

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