Theorem imnani

Description: Infer an implication from a negated conjunction. (Contributed by Mario Carneiro, 28-Sep-2015)

	Ref	Expression
Hypothesis	imnani.1	⊢ ¬ ( 𝜑 ∧ 𝜓 )
Assertion	imnani	⊢ ( 𝜑 → ¬ 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		imnani.1	⊢ ¬ ( 𝜑 ∧ 𝜓 )
2		imnan	⊢ ( ( 𝜑 → ¬ 𝜓 ) ↔ ¬ ( 𝜑 ∧ 𝜓 ) )
3	1 2	mpbir	⊢ ( 𝜑 → ¬ 𝜓 )