Theorem mpanlr1 667

Description: An inference based on modus ponens. (Contributed by NM, 30-Dec-2004.) (Proof shortened by Wolf Lammen, 7-Apr-2013.)

Hypotheses

Ref	Expression
mpanlr1.1	|- ps
mpanlr1.2	|- (((ph /\ (ps /\ ch)) /\ th) -> ta)

Assertion

Ref	Expression
mpanlr1	|- (((ph /\ ch) /\ th) -> ta)

Proof of Theorem mpanlr1

Step	Hyp	Ref	Expression
1		mpanlr1.1	. . 3 |- ps
2	1	jctl 525	. 2 |- (ch -> (ps /\ ch))
3		mpanlr1.2	. 2 |- (((ph /\ (ps /\ ch)) /\ th) -> ta)
4	2, 3	sylanl2 632	1 |- (((ph /\ ch) /\ th) -> ta)

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: (None)