Theorem neeq2i

Description: Inference for inequality. (Contributed by NM, 29-Apr-2005) (Proof shortened by Wolf Lammen, 19-Nov-2019)

	Ref	Expression
Hypothesis	neeq1i.1	⊢ 𝐴 = 𝐵
Assertion	neeq2i	⊢ ( 𝐶 ≠ 𝐴 ↔ 𝐶 ≠ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		neeq1i.1	⊢ 𝐴 = 𝐵
2	1	eqeq2i	⊢ ( 𝐶 = 𝐴 ↔ 𝐶 = 𝐵 )
3	2	necon3bii	⊢ ( 𝐶 ≠ 𝐴 ↔ 𝐶 ≠ 𝐵 )