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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	⊢ ¬ 𝜑
	Assertion	biorfi	⊢ ( 𝜓 ↔ ( 𝜑 ∨ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		biorfi.1	⊢ ¬ 𝜑
2		biorf	⊢ ( ¬ 𝜑 → ( 𝜓 ↔ ( 𝜑 ∨ 𝜓 ) ) )
3	1 2	ax-mp	⊢ ( 𝜓 ↔ ( 𝜑 ∨ 𝜓 ) )