Theorem pm3.43i 271

Description: Nested conjunction of antecedents. (Contributed by NM, 5-Aug-1993.)

Assertion

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

Proof of Theorem pm3.43i

Step	Hyp	Ref	Expression
1		pm3.2 138	. 2 |- ( ps -> ( ch -> ( ps /\ ch ) ) )
2	1	imim3i 61	1 |- ( ( ph -> ps ) -> ( ( ph -> ch ) -> ( ph -> ( ps /\ ch ) ) ) )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 107

This theorem is referenced by:  pm3.43  592