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Metamath Proof Explorer

Theorem anabss1

Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996) (Proof shortened by Wolf Lammen, 31-Dec-2012)

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

Proof

Step Hyp Ref Expression
1 anabss1.1 
 |-  ( ( ( ph /\ ps ) /\ ph ) -> ch )
2 1 an32s 
 |-  ( ( ( ph /\ ph ) /\ ps ) -> ch )
3 2 anabsan 
 |-  ( ( ph /\ ps ) -> ch )