Theorem neir

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

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

Proof

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