Theorem anabsan 504

Description: Absorption of antecedent with conjunction.

Hypothesis

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

Assertion

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

Proof of Theorem anabsan

Step	Hyp	Ref	Expression
1		anabsan.1	. . 3 |- (((ph /\ ph) /\ ps) -> ch)
2	1	an1rs 489	. 2 |- (((ph /\ ps) /\ ph) -> ch)
3	2	anabss1 499	1 |- ((ph /\ ps) -> ch)

Syntax hints:   -> wi 3   /\ wa 223

This theorem is referenced by:  anandis 512  prlem934b 5138  sq01t 6651  geoisumr 7243  idhme 10522

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