Theorem nsyli 133

Description: A negated syllogism inference. (Contributed by NM, 3-May-1994.)

Hypotheses

Ref	Expression
nsyli.1	|- (ph -> (ps -> ch))
nsyli.2	|- (th -> -. ch)

Assertion

Ref	Expression
nsyli	|- (ph -> (th -> -. ps))

Proof of Theorem nsyli

Step	Hyp	Ref	Expression
1		nsyli.2	. 2 |- (th -> -. ch)
2		nsyli.1	. . 3 |- (ph -> (ps -> ch))
3	2	con3d 125	. 2 |- (ph -> (-. ch -> -. ps))
4	1, 3	syl5 28	1 |- (ph -> (th -> -. ps))

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:  spimehOLD  1821