Theorem mpanl12

Description: An inference based on modus ponens. (Contributed by NM, 13-Jul-2005)

	Ref	Expression
Hypotheses	mpanl12.1	|- ph
	mpanl12.2	|- ps
	mpanl12.3	|- ( ( ( ph /\ ps ) /\ ch ) -> th )
Assertion	mpanl12	|- ( ch -> th )

Proof

Step	Hyp	Ref	Expression
1		mpanl12.1	|- ph
2		mpanl12.2	|- ps
3		mpanl12.3	|- ( ( ( ph /\ ps ) /\ ch ) -> th )
4	1 3	mpanl1	|- ( ( ps /\ ch ) -> th )
5	2 4	mpan	|- ( ch -> th )