Theorem nsyld 154

Description: A negated syllogism deduction. (Contributed by NM, 9-Apr-2005.)

Hypotheses

Ref	Expression
nsyld.1	|- ( ph -> ( ps -> -. ch ) )
nsyld.2	|- ( ph -> ( ta -> ch ) )

Assertion

Ref	Expression
nsyld	|- ( ph -> ( ps -> -. ta ) )

Proof of Theorem nsyld

Step	Hyp	Ref	Expression
1		nsyld.1	. 2 |- ( ph -> ( ps -> -. ch ) )
2		nsyld.2	. . 3 |- ( ph -> ( ta -> ch ) )
3	2	con3d 148	. 2 |- ( ph -> ( -. ch -> -. ta ) )
4	1, 3	syld 47	1 |- ( ph -> ( ps -> -. ta ) )

Syntax hints:   -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by:  pm2.65d  187  pltn2lp  16969  alexsubALTlem4  21854  eupth2eucrct  27077  ifeqeqx  29361  cvrat  34708  radcnvrat  38513