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Theorem nsyl3 627
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 626 1 (𝜒 → ¬ 𝜑)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 615  ax-in2 616
This theorem is referenced by:  con2i  628  nsyl  629  pm2.65i  640  cesare  2158  cesaro  2162  pwnss  4203  sucprcreg  4597  reg3exmidlemwe  4627  reldmtpos  6339  snexxph  7052  elfi2  7074  ismkvnex  7257  fzn  10164  seq3f1olemqsum  10658  pcmpt2  12667  elply2  15207
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