Theorem mp4an 654

Description: An inference based on modus ponens. (Contributed by Jeff Madsen, 15-Jun-2010.)

Hypotheses

Ref	Expression
mp4an.1	|- ph
mp4an.2	|- ps
mp4an.3	|- ch
mp4an.4	|- th
mp4an.5	|- (((ph /\ ps) /\ (ch /\ th)) -> ta)

Assertion

Ref	Expression
mp4an	|- ta

Proof of Theorem mp4an

Step	Hyp	Ref	Expression
1		mp4an.1	. . 3 |- ph
2		mp4an.2	. . 3 |- ps
3	1, 2	pm3.2i 441	. 2 |- (ph /\ ps)
4		mp4an.3	. . 3 |- ch
5		mp4an.4	. . 3 |- th
6	4, 5	pm3.2i 441	. 2 |- (ch /\ th)
7		mp4an.5	. 2 |- (((ph /\ ps) /\ (ch /\ th)) -> ta)
8	3, 6, 7	mp2an 653	1 |- ta

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:  tfin0c  4498  tc0c  6164  tcdi  6165  tc1c  6166