Theorem eqnetrri

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

	Ref	Expression
Hypotheses	eqnetrr.1	⊢ 𝐴 = 𝐵
	eqnetrr.2	⊢ 𝐴 ≠ 𝐶
Assertion	eqnetrri	⊢ 𝐵 ≠ 𝐶

Proof

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