Theorem mpanlr1 437

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 312	. 2 |- ( ch -> ( ps /\ ch ) )
3		mpanlr1.2	. 2 |- ( ( ( ph /\ ( ps /\ ch ) ) /\ th ) -> ta )
4	2, 3	sylanl2 401	1 |- ( ( ( ph /\ ch ) /\ th ) -> ta )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem is referenced by: (None)