Theorem nsyld 132

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 125	. 2 |- (ph -> (-. ch -> -. ta))
4	1, 3	syld 40	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  166  sbn  2062  enprmaplem3  6079  nnc3n3p1  6279