Theorem nsyli 121

Description: A negated syllogism inference.

Hypotheses

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

Assertion

Ref	Expression
nsyli	|- (ph -> (th -> -. ps))

Proof of Theorem nsyli

Step	Hyp	Ref	Expression
1		nsyli.1	. . 3 |- (ph -> (ps -> ch))
2	1	con3d 95	. 2 |- (ph -> (-. ch -> -. ps))
3		nsyli.2	. 2 |- (th -> -. ch)
4	2, 3	syl5 21	1 |- (ph -> (th -> -. ps))

Syntax hints:  -. wn 2   -> wi 3

This theorem is referenced by:  tz7.7 2968  tz7.48-2 3948  php 4499  nndomo 4506  isfinite2 4529  elirrv 4578  setind 4628  zorn2lem3 4770  alephval2 4882  bcthlem28 7976

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

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