Theorem mpanr1 664

Description: An inference based on modus ponens. (Contributed by NM, 3-May-1994.) (Proof shortened by Andrew Salmon, 7-May-2011.)

Hypotheses

Ref	Expression
mpanr1.1	|- ps
mpanr1.2	|- ((ph /\ (ps /\ ch)) -> th)

Assertion

Ref	Expression
mpanr1	|- ((ph /\ ch) -> th)

Proof of Theorem mpanr1

Step	Hyp	Ref	Expression
1		mpanr1.1	. 2 |- ps
2		mpanr1.2	. . 3 |- ((ph /\ (ps /\ ch)) -> th)
3	2	anassrs 629	. 2 |- (((ph /\ ps) /\ ch) -> th)
4	1, 3	mpanl2 662	1 |- ((ph /\ ch) -> 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:  mpanr12  666