Metamath Proof Explorer

Theorem an3

Description: A rearrangement of conjuncts. (Contributed by Rodolfo Medina, 25-Sep-2010)

Ref Expression
Assertion an3 
|- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) -> ( ph /\ th ) )

Proof

Step Hyp Ref Expression
1 an43 
 |-  ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ph /\ th ) /\ ( ps /\ ch ) ) )
2 1 simplbi 
 |-  ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) -> ( ph /\ th ) )