Theorem mpancom 650

Description: An inference based on modus ponens with commutation of antecedents. (Contributed by NM, 28-Oct-2003.) (Proof shortened by Wolf Lammen, 7-Apr-2013.)

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		id 19	. 2 |- (ps -> ps)
3		mpancom.2	. 2 |- ((ph /\ ps) -> ch)
4	1, 2, 3	syl2anc 642	1 |- (ps -> ch)

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:  mpan  651  spesbc  3127  nnc3n3p1  6278  nnc3n3p2  6279  nnc3p1n3p2  6280