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	$$⊢A\ne C$$
Assertion	eqnetrri	$$⊢B\ne C$$

Proof

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