Theorem anc2r 539

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		pm3.21 435	. . 3 |- (ph -> (ch -> (ch /\ ph)))
2	1	imim2d 48	. 2 |- (ph -> ((ps -> ch) -> (ps -> (ch /\ ph))))
3	2	a2i 12	1 |- ((ph -> (ps -> ch)) -> (ph -> (ps -> (ch /\ ph))))

Syntax hints:   -> wi 4   /\ wa 358

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 177  df-an 360

This theorem is referenced by: (None)