Metamath Proof Explorer

Theorem anc2r

Description: Conjoin antecedent to right of consequent in nested implication. (Contributed by NM, 15-Aug-1994)

Ref Expression
Assertion anc2r 
|- ( ( ph -> ( ps -> ch ) ) -> ( ph -> ( ps -> ( ch /\ ph ) ) ) )

Proof

Step Hyp Ref Expression
1 pm3.21 
 |-  ( ph -> ( ch -> ( ch /\ ph ) ) )
2 1 imim2d 
 |-  ( ph -> ( ( ps -> ch ) -> ( ps -> ( ch /\ ph ) ) ) )
3 2 a2i 
 |-  ( ( ph -> ( ps -> ch ) ) -> ( ph -> ( ps -> ( ch /\ ph ) ) ) )