Theorem neqne

Description: From non-equality to inequality. (Contributed by Glauco Siliprandi, 11-Dec-2019)

	Ref	Expression
Assertion	neqne	⊢ ( ¬ 𝐴 = 𝐵 → 𝐴 ≠ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( ¬ 𝐴 = 𝐵 → ¬ 𝐴 = 𝐵 )
2	1	neqned	⊢ ( ¬ 𝐴 = 𝐵 → 𝐴 ≠ 𝐵 )