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Metamath Proof Explorer

Theorem impancom

Description: Mixed importation/commutation inference. (Contributed by NM, 22-Jun-2013)

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

Proof

Step Hyp Ref Expression
1 impancom.1 
 |-  ( ( ph /\ ps ) -> ( ch -> th ) )
2 1 ex 
 |-  ( ph -> ( ps -> ( ch -> th ) ) )
3 2 com23 
 |-  ( ph -> ( ch -> ( ps -> th ) ) )
4 3 imp 
 |-  ( ( ph /\ ch ) -> ( ps -> th ) )