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Theorem dfnot 1244
Description: One definition of negation in logics that take as axiomatic is via "implies contradiction", i.e. φ → ⊥. (Contributed by Mario Carneiro, 2-Feb-2015.)
Assertion
Ref Expression
dfnot φ ↔ (φ → ⊥ ))

Proof of Theorem dfnot
StepHypRef Expression
1 fal 1234 . 2 ¬ ⊥
2 mtt 597 . 2 (¬ ⊥ → (¬ φ ↔ (φ → ⊥ )))
31, 2ax-mp 7 1 φ ↔ (φ → ⊥ ))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 98  wfal 1229
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 532  ax-in2 533
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-fal 1232
This theorem is referenced by:  inegd  1245  pclem6  1247  alnex  1368  alexim  1519  difin  3152  indifdir  3171
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