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Theorem inegd 1263
 Description: Negation introduction rule from natural deduction. (Contributed by Mario Carneiro, 9-Feb-2017.)
Hypothesis
Ref Expression
inegd.1 ((𝜑𝜓) → ⊥)
Assertion
Ref Expression
inegd (𝜑 → ¬ 𝜓)

Proof of Theorem inegd
StepHypRef Expression
1 inegd.1 . . 3 ((𝜑𝜓) → ⊥)
21ex 108 . 2 (𝜑 → (𝜓 → ⊥))
3 dfnot 1262 . 2 𝜓 ↔ (𝜓 → ⊥))
42, 3sylibr 137 1 (𝜑 → ¬ 𝜓)
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 97  ⊥wfal 1248 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 1246  df-fal 1249 This theorem is referenced by:  genpdisj  6621  cauappcvgprlemdisj  6749  caucvgprlemdisj  6772  caucvgprprlemdisj  6800  resqrexlemgt0  9618  resqrexlemoverl  9619  leabs  9672  climge0  9845
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