Metamath Proof Explorer


Theorem 3com23

Description: Commutation in antecedent. Swap 2nd and 3rd. (Contributed by NM, 28-Jan-1996) (Proof shortened by Wolf Lammen, 9-Apr-2022)

Ref Expression
Hypothesis 3exp.1
|- ( ( ph /\ ps /\ ch ) -> th )
Assertion 3com23
|- ( ( ph /\ ch /\ ps ) -> th )

Proof

Step Hyp Ref Expression
1 3exp.1
 |-  ( ( ph /\ ps /\ ch ) -> th )
2 1 3comr
 |-  ( ( ch /\ ph /\ ps ) -> th )
3 2 3com12
 |-  ( ( ph /\ ch /\ ps ) -> th )