Metamath Proof Explorer


Theorem imp43

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

Ref Expression
Hypothesis imp4.1
|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
Assertion imp43
|- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) -> ta )

Proof

Step Hyp Ref Expression
1 imp4.1
 |-  ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
2 1 imp4b
 |-  ( ( ph /\ ps ) -> ( ( ch /\ th ) -> ta ) )
3 2 imp
 |-  ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) -> ta )