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Theorem inegd 1350
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 114 . 2 (𝜑 → (𝜓 → ⊥))
3 dfnot 1349 . 2 𝜓 ↔ (𝜓 → ⊥))
42, 3sylibr 133 1 (𝜑 → ¬ 𝜓)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wa 103  wfal 1336
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-fal 1337
This theorem is referenced by:  genpdisj  7338  cauappcvgprlemdisj  7466  caucvgprlemdisj  7489  caucvgprprlemdisj  7517  suplocexprlemdisj  7535  suplocexprlemub  7538  suplocsrlem  7623  resqrexlemgt0  10799  resqrexlemoverl  10800  leabs  10853  climge0  11101  ennnfonelemex  11934  dedekindeu  12780  dedekindicclemicc  12789
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