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Metamath Proof Explorer

Theorem nbfal

Description: The negation of a proposition is equivalent to itself being equivalent to F. . (Contributed by Anthony Hart, 14-Aug-2011)

Ref Expression
Assertion nbfal ⊢ ¬ φ ↔ φ ↔ ⊥

Proof

Step Hyp Ref Expression
1 fal ⊢ ¬ ⊥
2 1 nbn ⊢ ¬ φ ↔ φ ↔ ⊥