Theorem neeqtri

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

	Ref	Expression
Hypotheses	neeqtr.1	$$⊢A\ne B$$
	neeqtr.2	$$⊢B=C$$
Assertion	neeqtri	$$⊢A\ne C$$

Proof

Step	Hyp	Ref	Expression
1		neeqtr.1	$$⊢A\ne B$$
2		neeqtr.2	$$⊢B=C$$
3	2	neeq2i	$$⊢A\ne B\leftrightarrow A\ne C$$
4	1 3	mpbi	$$⊢A\ne C$$