Theorem nsyl3 111

Description: A negated syllogism inference. (Contributed by NM, 1-Dec-1995.)

Hypotheses

Ref	Expression
nsyl3.1	|- (ph -> -. ps)
nsyl3.2	|- (ch -> ps)

Assertion

Ref	Expression
nsyl3	|- (ch -> -. ph)

Proof of Theorem nsyl3

Step	Hyp	Ref	Expression
1		nsyl3.2	. 2 |- (ch -> ps)
2		nsyl3.1	. . 3 |- (ph -> -. ps)
3	2	a1i 10	. 2 |- (ch -> (ph -> -. ps))
4	1, 3	mt2d 109	1 |- (ch -> -. ph)

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:  con2i  112  nsyl  113  ax9  1949  cesare  2307  cesaro  2311