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 ↔ ⊥ )