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Metamath Proof Explorer

Theorem biorfriOLD

Description: Obsolete version of biorfri as of 10-Aug-2025. A wff is equivalent to its disjunction with falsehood. (Contributed by NM, 23-Mar-1995) (Proof shortened by Wolf Lammen, 16-Jul-2021) (New usage is discouraged.) (Proof modification is discouraged.)

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

Proof

Step	Hyp	Ref	Expression
1		biorfi.1	$⊢ \neg φ$
2		orc	$⊢ ψ \to (ψ \lor φ)$
3		pm2.53	$⊢ (ψ \lor φ) \to (\neg ψ \to φ)$
4	1 3	mt3i	$⊢ (ψ \lor φ) \to ψ$
5	2 4	impbii	$⊢ ψ \leftrightarrow (ψ \lor φ)$