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Metamath Proof Explorer

Theorem imp44

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

Ref Expression
Hypothesis imp4.1 
|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
Assertion imp44 
|- ( ( ph /\ ( ( ps /\ ch ) /\ th ) ) -> ta )

Proof

Step Hyp Ref Expression
1 imp4.1 
 |-  ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
2 1 imp4c 
 |-  ( ph -> ( ( ( ps /\ ch ) /\ th ) -> ta ) )
3 2 imp 
 |-  ( ( ph /\ ( ( ps /\ ch ) /\ th ) ) -> ta )