Metamath Proof Explorer

Theorem pm3.43i

Description: Nested conjunction of antecedents. (Contributed by NM, 4-Jan-1993)

Ref Expression
Assertion pm3.43i 
|- ( ( ph -> ps ) -> ( ( ph -> ch ) -> ( ph -> ( ps /\ ch ) ) ) )

Proof

Step Hyp Ref Expression
1 pm3.2 
 |-  ( ps -> ( ch -> ( ps /\ ch ) ) )
2 1 imim3i 
 |-  ( ( ph -> ps ) -> ( ( ph -> ch ) -> ( ph -> ( ps /\ ch ) ) ) )