Theorem mpan22 532

Description: An inference based on modus ponens.

Hypotheses

Ref	Expression
mpan22.1	|- ch
mpan22.2	|- ((ph /\ (ps /\ ch)) -> th)

Assertion

Ref	Expression
mpan22	|- ((ph /\ ps) -> th)

Proof of Theorem mpan22

Step	Hyp	Ref	Expression
1		mpan22.1	. . 3 |- ch
2		mpan22.2	. . . 4 |- ((ph /\ (ps /\ ch)) -> th)
3	2	exp 291	. . 3 |- (ph -> ((ps /\ ch) -> th))
4	1, 3	mpan2i 522	. 2 |- (ph -> (ps -> th))
5	4	imp 277	1 |- ((ph /\ ps) -> th)

Syntax hints:   -> wi 2   /\ wa 196

This theorem is referenced by:  aceq6b 3565  prlem934b 3932  rimul 4534

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

metamath.org