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Metamath Proof Explorer

Theorem biortn

Description: A wff is equivalent to its negated disjunction with falsehood. (Contributed by NM, 9-Jul-2012)

		Ref	Expression
	Assertion	biortn	$⊢ φ \to (ψ \leftrightarrow (\neg φ \lor ψ))$

Step	Hyp	Ref	Expression
1		notnot	$⊢ φ \to \neg \neg φ$
2		biorf	$⊢ \neg \neg φ \to (ψ \leftrightarrow (\neg φ \lor ψ))$
3	1 2	syl	$⊢ φ \to (ψ \leftrightarrow (\neg φ \lor ψ))$