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Theorem nsyl3 591
Description: A negated syllogism inference. (Contributed by NM, 1-Dec-1995.) (Revised by NM, 13-Jun-2013.)
Hypotheses
Ref Expression
nsyl3.1 (𝜑 → ¬ 𝜓)
nsyl3.2 (𝜒𝜓)
Assertion
Ref Expression
nsyl3 (𝜒 → ¬ 𝜑)

Proof of Theorem nsyl3
StepHypRef Expression
1 nsyl3.2 . 2 (𝜒𝜓)
2 nsyl3.1 . . 3 (𝜑 → ¬ 𝜓)
32a1i 9 . 2 (𝜒 → (𝜑 → ¬ 𝜓))
41, 3mt2d 590 1 (𝜒 → ¬ 𝜑)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-in1 579  ax-in2 580
This theorem is referenced by:  con2i  592  nsyl  593  pm2.65i  603  cesare  2052  cesaro  2056  pwnss  3994  sucprcreg  4365  reg3exmidlemwe  4394  reldmtpos  6018  snexxph  6657  fzn  9454  seq3f1olemqsum  9925
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