Theorem mpanl2

Description: An inference based on modus ponens. (Contributed by NM, 16-Aug-1994) (Proof shortened by Andrew Salmon, 7-May-2011)

	Ref	Expression
Hypotheses	mpanl2.1	|- ps
	mpanl2.2	|- ( ( ( ph /\ ps ) /\ ch ) -> th )
Assertion	mpanl2	|- ( ( ph /\ ch ) -> th )

Proof

Step	Hyp	Ref	Expression
1		mpanl2.1	|- ps
2		mpanl2.2	|- ( ( ( ph /\ ps ) /\ ch ) -> th )
3	1	jctr	|- ( ph -> ( ph /\ ps ) )
4	3 2	sylan	|- ( ( ph /\ ch ) -> th )