Theorem mpsylsyld 69

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

Hypotheses

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

Assertion

Ref	Expression
mpsylsyld	|- ( ps -> ( ch -> ta ) )

Proof of Theorem mpsylsyld

Step	Hyp	Ref	Expression
1		mpsylsyld.1	. . 3 |- ph
2	1	a1i 11	. 2 |- ( ps -> ph )
3		mpsylsyld.2	. 2 |- ( ps -> ( ch -> th ) )
4		mpsylsyld.3	. 2 |- ( ph -> ( th -> ta ) )
5	2, 3, 4	sylsyld 61	1 |- ( ps -> ( ch -> ta ) )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  vk15.4j  38734  onfrALTlem3  38759  ee02an  38924