Metamath Proof Explorer

Theorem 3impb

Description: Importation from double to triple conjunction. (Contributed by NM, 20-Aug-1995)

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

Proof

Step Hyp Ref Expression
1 3impb.1 
 |-  ( ( ph /\ ( ps /\ ch ) ) -> th )
2 1 exp32 
 |-  ( ph -> ( ps -> ( ch -> th ) ) )
3 2 3imp 
 |-  ( ( ph /\ ps /\ ch ) -> th )