Theorem anabss1 499

Description: Absorption of antecedent into conjunction.

Hypothesis

Ref	Expression
anabss1.1	|- (((ph /\ ps) /\ ph) -> ch)

Assertion

Ref	Expression
anabss1	|- ((ph /\ ps) -> ch)

Proof of Theorem anabss1

Step	Hyp	Ref	Expression
1		anabss1.1	. . 3 |- (((ph /\ ps) /\ ph) -> ch)
2	1	adantrr 395	. 2 |- (((ph /\ ps) /\ (ph /\ ps)) -> ch)
3	2	anidms 434	1 |- ((ph /\ ps) -> ch)

Syntax hints:   -> wi 3   /\ wa 223

This theorem is referenced by:  anabss4 501  anabsan 504  pm5.54 683  ordtri3or 2979  omordi 4197

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