Theorem nsyl4 105

Description: A negated syllogism inference.

Hypotheses

Ref	Expression
nsyl4.1	|- (ph -> ps)
nsyl4.2	|- (-. ph -> ch)

Assertion

Ref	Expression
nsyl4	|- (-. ch -> ps)

Proof of Theorem nsyl4

Step	Hyp	Ref	Expression
1		nsyl4.2	. . 3 |- (-. ph -> ch)
2	1	con1i 88	. 2 |- (-. ch -> ph)
3		nsyl4.1	. 2 |- (ph -> ps)
4	2, 3	syl 12	1 |- (-. ch -> ps)

Syntax hints:  -. wn 1   -> wi 2

This theorem is referenced by:  pm5.18 497  hbne 699  eq4ds 823  tz6.12i 2847  eceqopreq 3249

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

metamath.org