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Theorem nbn3 624
Description: Transfer falsehood via equivalence. (Contributed by NM, 11-Sep-2006.)
Hypothesis
Ref Expression
nbn3.1 𝜑
Assertion
Ref Expression
nbn3 𝜓 ↔ (𝜓 ↔ ¬ 𝜑))

Proof of Theorem nbn3
StepHypRef Expression
1 nbn3.1 . . 3 𝜑
21notnoti 582 . 2 ¬ ¬ 𝜑
32nbn 623 1 𝜓 ↔ (𝜓 ↔ ¬ 𝜑))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 552  ax-in2 553
This theorem depends on definitions:  df-bi 114
This theorem is referenced by: (None)
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