Theorem neeq1i

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	neeq1i	⊢ ( 𝐴 ≠ 𝐶 ↔ 𝐵 ≠ 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		neeq1i.1	⊢ 𝐴 = 𝐵
2	1	eqeq1i	⊢ ( 𝐴 = 𝐶 ↔ 𝐵 = 𝐶 )
3	2	necon3bii	⊢ ( 𝐴 ≠ 𝐶 ↔ 𝐵 ≠ 𝐶 )