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Theorem nbn 336
Description: The negation of a wff is equivalent to the wff's equivalence to falsehood. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 3-Oct-2013.)
Hypothesis
Ref Expression
nbn.1 ¬ φ
Assertion
Ref Expression
nbn ψ ↔ (ψφ))

Proof of Theorem nbn
StepHypRef Expression
1 nbn.1 . . 3 ¬ φ
2 bibif 335 . . 3 φ → ((ψφ) ↔ ¬ ψ))
31, 2ax-mp 5 . 2 ((ψφ) ↔ ¬ ψ)
43bicomi 193 1 ψ ↔ (ψφ))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 176
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177
This theorem is referenced by:  nbn3  337  nbfal  1325  n0f  3558  dm0rn0  4921  dmeq0  4922
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