Theorem anabss3 382

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 311	. 2 |- (((ph /\ ps) /\ (ph /\ ps)) -> ch)
3	2	anidms 332	1 |- ((ph /\ ps) -> ch)

Syntax hints:   -> wi 2   /\ wa 196

This theorem is referenced by:  anabsan2 387  ordin 2228  rdglimt 2986

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

metamath.org