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Metamath Proof Explorer

Theorem bifal

Description: A contradiction is equivalent to falsehood. (Contributed by Mario Carneiro, 9-May-2015)

Ref Expression
Hypothesis bifal.1 ⊢ ¬ 𝜑
Assertion bifal ( 𝜑 ↔ ⊥ )

Proof

Step Hyp Ref Expression
1 bifal.1 ⊢ ¬ 𝜑
2 fal ⊢ ¬ ⊥
3 1 2 2false ⊢ ( 𝜑 ↔ ⊥ )