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Metamath Proof Explorer

Theorem imp42

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

Ref Expression
Hypothesis imp4.1 
|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
Assertion imp42 
|- ( ( ( ph /\ ( ps /\ ch ) ) /\ th ) -> ta )

Proof

Step Hyp Ref Expression
1 imp4.1 
 |-  ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
2 1 imp32 
 |-  ( ( ph /\ ( ps /\ ch ) ) -> ( th -> ta ) )
3 2 imp 
 |-  ( ( ( ph /\ ( ps /\ ch ) ) /\ th ) -> ta )