Theorem mpanr2OLD 777

Description: An inference based on modus ponens.

Hypotheses

Ref	Expression
mpanr2.1	|- ch
mpanr2.2	|- ((ph /\ (ps /\ ch)) -> th)

Assertion

Ref	Expression
mpanr2OLD	|- ((ph /\ ps) -> th)

Proof of Theorem mpanr2OLD

Step	Hyp	Ref	Expression
1		mpanr2.1	. . 3 |- ch
2		mpanr2.2	. . . 4 |- ((ph /\ (ps /\ ch)) -> th)
3	2	ex 402	. . 3 |- (ph -> ((ps /\ ch) -> th))
4	1, 3	mpan2i 763	. 2 |- (ph -> (ps -> th))
5	4	imp 377	1 |- ((ph /\ ps) -> th)

Syntax hints:   -> wi 3   /\ wa 240

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 164  df-an 242

Copyright terms: Public domain