Theorem nsyl2 119

Description: A negated syllogism inference. (Contributed by NM, 26-Jun-1994.)

Hypotheses

Ref	Expression
nsyl2.1	|- (ph -> -. ps)
nsyl2.2	|- (-. ch -> ps)

Assertion

Ref	Expression
nsyl2	|- (ph -> ch)

Proof of Theorem nsyl2

Step	Hyp	Ref	Expression
1		nsyl2.1	. 2 |- (ph -> -. ps)
2		nsyl2.2	. . 3 |- (-. ch -> ps)
3	2	a1i 10	. 2 |- (ph -> (-. ch -> ps))
4	1, 3	mt3d 117	1 |- (ph -> ch)

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:  con1i  121  con4i  122  dvelimv  1939  ecexr  5951