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Metamath Proof Explorer

Theorem impd

Description: Importation deduction. (Contributed by NM, 31-Mar-1994)

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

Proof

Step Hyp Ref Expression
1 impd.1 
 |-  ( ph -> ( ps -> ( ch -> th ) ) )
2 1 com3l 
 |-  ( ps -> ( ch -> ( ph -> th ) ) )
3 2 imp 
 |-  ( ( ps /\ ch ) -> ( ph -> th ) )
4 3 com12 
 |-  ( ph -> ( ( ps /\ ch ) -> th ) )