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Metamath Proof Explorer

Theorem anabsan2

Description: Absorption of antecedent with conjunction. (Contributed by NM, 10-May-2004)

Ref Expression
Hypothesis anabsan2.1 
|- ( ( ph /\ ( ps /\ ps ) ) -> ch )
Assertion anabsan2 
|- ( ( ph /\ ps ) -> ch )

Proof

Step Hyp Ref Expression
1 anabsan2.1 
 |-  ( ( ph /\ ( ps /\ ps ) ) -> ch )
2 1 an12s 
 |-  ( ( ps /\ ( ph /\ ps ) ) -> ch )
3 2 anabss7 
 |-  ( ( ph /\ ps ) -> ch )