Theorem mpanr12 666

Description: An inference based on modus ponens. (Contributed by NM, 24-Jul-2009.)

Hypotheses

Ref	Expression
mpanr12.1	|- ps
mpanr12.2	|- ch
mpanr12.3	|- ((ph /\ (ps /\ ch)) -> th)

Assertion

Ref	Expression
mpanr12	|- (ph -> th)

Proof of Theorem mpanr12

Step	Hyp	Ref	Expression
1		mpanr12.2	. 2 |- ch
2		mpanr12.1	. . 3 |- ps
3		mpanr12.3	. . 3 |- ((ph /\ (ps /\ ch)) -> th)
4	2, 3	mpanr1 664	. 2 |- ((ph /\ ch) -> th)
5	1, 4	mpan2 652	1 |- (ph -> 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:  sbthlem1  6203