Theorem nsyld 117

Description: A negated syllogism deduction.

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 95	. 2 |- (ph -> (-. ch -> -. ta))
4	1, 3	syld 27	1 |- (ph -> (ps -> -. ta))

Syntax hints:  -. wn 2   -> wi 3

This theorem is referenced by:  sbn 1231  nlimsucg 3112  caucvglem6 7162  bcthlem29 8027

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

Copyright terms: Public domain