Theorem neii

Description: Inference associated with df-ne . (Contributed by BJ, 7-Jul-2018)

	Ref	Expression
Hypothesis	neii.1	⊢ 𝐴 ≠ 𝐵
Assertion	neii	⊢ ¬ 𝐴 = 𝐵

Proof

Step	Hyp	Ref	Expression
1		neii.1	⊢ 𝐴 ≠ 𝐵
2		df-ne	⊢ ( 𝐴 ≠ 𝐵 ↔ ¬ 𝐴 = 𝐵 )
3	1 2	mpbi	⊢ ¬ 𝐴 = 𝐵