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Metamath Proof Explorer

Theorem imp32

Description: An importation inference. (Contributed by NM, 26-Apr-1994)

Ref Expression
Hypothesis imp31.1 
|- ( ph -> ( ps -> ( ch -> th ) ) )
Assertion imp32 
|- ( ( ph /\ ( ps /\ ch ) ) -> th )

Proof

Step Hyp Ref Expression
1 imp31.1 
 |-  ( ph -> ( ps -> ( ch -> th ) ) )
2 1 impd 
 |-  ( ph -> ( ( ps /\ ch ) -> th ) )
3 2 imp 
 |-  ( ( ph /\ ( ps /\ ch ) ) -> th )