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Metamath Proof Explorer

Theorem nbn3

Description: Transfer falsehood via equivalence. (Contributed by NM, 11-Sep-2006)

		Ref	Expression
	Hypothesis	nbn3.1	⊢ 𝜑
	Assertion	nbn3	⊢ ( ¬ 𝜓 ↔ ( 𝜓 ↔ ¬ 𝜑 ) )

Step	Hyp	Ref	Expression
1		nbn3.1	⊢ 𝜑
2	1	notnoti	⊢ ¬ ¬ 𝜑
3	2	nbn	⊢ ( ¬ 𝜓 ↔ ( 𝜓 ↔ ¬ 𝜑 ) )