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Metamath Proof Explorer

Theorem biorfi

Description: The dual of biorf is not biantr but iba (and ibar ). So there should also be a "biorfr". (Note that these four statements can actually be strengthened to biconditionals.) (Contributed by BJ, 26-Oct-2019)

		Ref	Expression
	Hypothesis	biorfi.1	$⊢ \neg φ$
	Assertion	biorfi	$⊢ ψ \leftrightarrow (φ \lor ψ)$

Proof

Step	Hyp	Ref	Expression
1		biorfi.1	$⊢ \neg φ$
2		biorf	$⊢ \neg φ \to (ψ \leftrightarrow (φ \lor ψ))$
3	1 2	ax-mp	$⊢ ψ \leftrightarrow (φ \lor ψ)$