Metamath Proof Explorer


Theorem 3imp

Description: Importation inference. (Contributed by NM, 8-Apr-1994) (Proof shortened by Wolf Lammen, 20-Jun-2022)

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

Proof

Step Hyp Ref Expression
1 3imp.1
 |-  ( ph -> ( ps -> ( ch -> th ) ) )
2 1 imp31
 |-  ( ( ( ph /\ ps ) /\ ch ) -> th )
3 2 3impa
 |-  ( ( ph /\ ps /\ ch ) -> th )