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Metamath Proof Explorer

Theorem 3imp1

Description: Importation to left triple conjunction. (Contributed by NM, 24-Feb-2005)

Ref Expression
Hypothesis 3imp1.1 
|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
Assertion 3imp1 
|- ( ( ( ph /\ ps /\ ch ) /\ th ) -> ta )

Proof

Step Hyp Ref Expression
1 3imp1.1 
 |-  ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
2 1 3imp 
 |-  ( ( ph /\ ps /\ ch ) -> ( th -> ta ) )
3 2 imp 
 |-  ( ( ( ph /\ ps /\ ch ) /\ th ) -> ta )