Theorem nsyl3 104

Description: A negated syllogism inference.

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	con2i 89	. 2 |- (ps -> -. ph)
4	1, 3	syl 12	1 |- (ch -> -. ph)

Syntax hints:  -. wn 1   -> wi 2

This theorem is referenced by:  sdomirr 3314  sucprcreg 3451  cardnn 3631  add20 4329

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

metamath.org