Theorem nsyl2 118

Description: A negated syllogism inference.

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	con1i 96	. 2 |- (-. ps -> ch)
4	1, 3	syl 10	1 |- (ph -> ch)

Syntax hints:  -. wn 2   -> wi 3

This theorem is referenced by:  tfi 3116  rankel 4652  r1pwcl 4659  card1 4805  alephnbtwn 4840  ivthlem7 7222  ivthlem7OLD 7231  hmdmadjt 9780

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

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