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Metamath Proof Explorer

Theorem pm5.21im

Description: Two propositions are equivalent if they are both false. Closed form of 2false . Equivalent to a biimpr -like version of the xor-connective. (Contributed by Wolf Lammen, 13-May-2013)

		Ref	Expression
	Assertion	pm5.21im	⊢ ( ¬ 𝜑 → ( ¬ 𝜓 → ( 𝜑 ↔ 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		nbn2	⊢ ( ¬ 𝜑 → ( ¬ 𝜓 ↔ ( 𝜑 ↔ 𝜓 ) ) )
2	1	biimpd	⊢ ( ¬ 𝜑 → ( ¬ 𝜓 → ( 𝜑 ↔ 𝜓 ) ) )