Theorem neeqtrri

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

	Ref	Expression
Hypotheses	neeqtrr.1	$$⊢A\ne B$$
	neeqtrr.2	$$⊢C=B$$
Assertion	neeqtrri	$$⊢A\ne C$$

Proof

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