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Theorem inegd 1262
Description: Negation introduction rule from natural deduction. (Contributed by Mario Carneiro, 9-Feb-2017.)
Hypothesis
Ref Expression
inegd.1 ((φ ψ) → ⊥ )
Assertion
Ref Expression
inegd (φ → ¬ ψ)

Proof of Theorem inegd
StepHypRef Expression
1 inegd.1 . . 3 ((φ ψ) → ⊥ )
21ex 108 . 2 (φ → (ψ → ⊥ ))
3 dfnot 1261 . 2 ψ ↔ (ψ → ⊥ ))
42, 3sylibr 137 1 (φ → ¬ ψ)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   wa 97  wfal 1247
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248
This theorem is referenced by:  genpdisj  6506
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