Theorem bifal

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

	Ref	Expression
Hypothesis	bifal.1	$$⊢\neg \phi$$
Assertion	bifal	$$⊢\phi \leftrightarrow \perp$$

Proof

Step	Hyp	Ref	Expression
1		bifal.1	$$⊢\neg \phi$$
2		fal	$$⊢\neg \perp$$
3	1 2	2false	$$⊢\phi \leftrightarrow \perp$$