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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	$⊢ \neg φ$
	Assertion	bifal	$⊢ φ \leftrightarrow ⊥$

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