Theorem nanan

Description: Conjunction in terms of alternative denial. (Contributed by Mario Carneiro, 9-May-2015)

	Ref	Expression
Assertion	nanan	⊢ ( ( 𝜑 ∧ 𝜓 ) ↔ ¬ ( 𝜑 ⊼ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		df-nan	⊢ ( ( 𝜑 ⊼ 𝜓 ) ↔ ¬ ( 𝜑 ∧ 𝜓 ) )
2	1	con2bii	⊢ ( ( 𝜑 ∧ 𝜓 ) ↔ ¬ ( 𝜑 ⊼ 𝜓 ) )