Theorem mpancom 528

Description: An inference based on modus ponens with commutation of antecedents.

Hypotheses

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

Assertion

Ref	Expression
mpancom	|- (ps -> ch)

Proof of Theorem mpancom

Step	Hyp	Ref	Expression
1		mpancom.1	. 2 |- (ps -> ph)
2		mpancom.2	. . 3 |- ((ph /\ ps) -> ch)
3	2	ancoms 334	. 2 |- ((ps /\ ph) -> ch)
4	1, 3	mpdan 527	1 |- (ps -> ch)

Syntax hints:   -> wi 2   /\ wa 196

This theorem is referenced by:  reuuni3 1958  orduniorsuc 2337  cardnn 3631  ondomcard 3663  ltexprlem4 3939  flidt 4627

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