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Metamath Proof Explorer

Theorem imdistani

Description: Distribution of implication with conjunction. (Contributed by NM, 1-Aug-1994)

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

Proof

Step Hyp Ref Expression
1 imdistani.1 
 |-  ( ph -> ( ps -> ch ) )
2 1 anc2li 
 |-  ( ph -> ( ps -> ( ph /\ ch ) ) )
3 2 imp 
 |-  ( ( ph /\ ps ) -> ( ph /\ ch ) )