Theorem mp2and 660

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

Hypotheses

Ref	Expression
mp2and.1	|- (ph -> ps)
mp2and.2	|- (ph -> ch)
mp2and.3	|- (ph -> ((ps /\ ch) -> th))

Assertion

Ref	Expression
mp2and	|- (ph -> th)

Proof of Theorem mp2and

Step	Hyp	Ref	Expression
1		mp2and.2	. 2 |- (ph -> ch)
2		mp2and.1	. . 3 |- (ph -> ps)
3		mp2and.3	. . 3 |- (ph -> ((ps /\ ch) -> th))
4	2, 3	mpand 656	. 2 |- (ph -> (ch -> th))
5	1, 4	mpd 14	1 |- (ph -> th)

Syntax hints:   -> wi 4   /\ wa 358

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

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  ssnelpssd  3614  nnsucelr  4428  sfinltfin  4535  vfinncvntnn  4548  trd  5921  frd  5922  antid  5929