Metamath Proof Explorer


Theorem an12s

Description: Swap two conjuncts in antecedent. The label suffix "s" means that an12 is combined with syl (or a variant). (Contributed by NM, 13-Mar-1996)

Ref Expression
Hypothesis an12s.1
|- ( ( ph /\ ( ps /\ ch ) ) -> th )
Assertion an12s
|- ( ( ps /\ ( ph /\ ch ) ) -> th )

Proof

Step Hyp Ref Expression
1 an12s.1
 |-  ( ( ph /\ ( ps /\ ch ) ) -> th )
2 an12
 |-  ( ( ps /\ ( ph /\ ch ) ) <-> ( ph /\ ( ps /\ ch ) ) )
3 2 1 sylbi
 |-  ( ( ps /\ ( ph /\ ch ) ) -> th )