Theorem neeqtrri

Description: Substitution of equal classes into an inequality. (Contributed by NM, 4-Jul-2012)

	Ref	Expression
Hypotheses	neeqtrr.1	⊢ 𝐴 ≠ 𝐵
	neeqtrr.2	⊢ 𝐶 = 𝐵
Assertion	neeqtrri	⊢ 𝐴 ≠ 𝐶

Proof

Step	Hyp	Ref	Expression
1		neeqtrr.1	⊢ 𝐴 ≠ 𝐵
2		neeqtrr.2	⊢ 𝐶 = 𝐵
3	2	eqcomi	⊢ 𝐵 = 𝐶
4	1 3	neeqtri	⊢ 𝐴 ≠ 𝐶