Theorem mpsylsyld

Description: Modus ponens combined with a double syllogism inference. (Contributed by Alan Sare, 22-Jul-2012)

	Ref	Expression
Hypotheses	mpsylsyld.1	|- ph
	mpsylsyld.2	|- ( ps -> ( ch -> th ) )
	mpsylsyld.3	|- ( ph -> ( th -> ta ) )
Assertion	mpsylsyld	|- ( ps -> ( ch -> ta ) )

Proof

Step	Hyp	Ref	Expression
1		mpsylsyld.1	|- ph
2		mpsylsyld.2	|- ( ps -> ( ch -> th ) )
3		mpsylsyld.3	|- ( ph -> ( th -> ta ) )
4	1	a1i	|- ( ps -> ph )
5	4 2 3	sylsyld	|- ( ps -> ( ch -> ta ) )