Theorem nsyl4 120

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 96	. 2 |- (-. ch -> ph)
3		nsyl4.1	. 2 |- (ph -> ps)
4	2, 3	syl 10	1 |- (-. ch -> ps)

Syntax hints:  -. wn 2   -> wi 3

This theorem is referenced by:  ax6o 977  ax6 979  ax467 1023  ax467to7 1026  nalequcoms 1144  eceqopreq 4313

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

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