Theorem mpan2d 655

Description: A deduction based on modus ponens. (Contributed by NM, 12-Dec-2004.)

Hypotheses

Ref	Expression
mpan2d.1	|- (ph -> ch)
mpan2d.2	|- (ph -> ((ps /\ ch) -> th))

Assertion

Ref	Expression
mpan2d	|- (ph -> (ps -> th))

Proof of Theorem mpan2d

Step	Hyp	Ref	Expression
1		mpan2d.1	. 2 |- (ph -> ch)
2		mpan2d.2	. . 3 |- (ph -> ((ps /\ ch) -> th))
3	2	exp3a 425	. 2 |- (ph -> (ps -> (ch -> th)))
4	1, 3	mpid 37	1 |- (ph -> (ps -> th))

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:  mpand  656  mpan2i  658  ltfintri  4466  leconnnc  6218  nclenn  6249  ncslesuc  6267  nchoicelem4  6292