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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
StepHypRef Expression
1 nsyli.1 . . 3 |- (ph -> (ps -> ch))
21con3d 95 . 2 |- (ph -> (-. ch -> -. ps))
3 nsyli.2 . 2 |- (th -> -. ch)
42, 3syl5 21 1 |- (ph -> (th -> -. ps))
Colors of variables: wff set class
Syntax hints:  -. wn 2   -> wi 3
This theorem is referenced by:  tz7.7 2963  tz7.48-2 3942  php 4493  nndomo 4500  isfinite2 4523  elirrv 4570  setind 4620  zorn2lem3 4762  alephval2 4874  bcthlem28 7960
This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7
Copyright terms: Public domain