Metamath Proof Explorer

Theorem 3expb

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

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

Proof

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