Theorem anc2r 579

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

Assertion

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

Proof of Theorem anc2r

Step	Hyp	Ref	Expression
1		pm3.21 464	. . 3 |- ( ph -> ( ch -> ( ch /\ ph ) ) )
2	1	imim2d 57	. 2 |- ( ph -> ( ( ps -> ch ) -> ( ps -> ( ch /\ ph ) ) ) )
3	2	a2i 14	1 |- ( ( ph -> ( ps -> ch ) ) -> ( ph -> ( ps -> ( ch /\ ph ) ) ) )

Syntax hints:   -> wi 4   /\ wa 384

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386

This theorem is referenced by:  ssorduni  6985