Theorem mpanlr1

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

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

Proof

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