Theorem eqnetri

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

	Ref	Expression
Hypotheses	eqnetr.1	$$⊢A=B$$
	eqnetr.2	$$⊢B\ne C$$
Assertion	eqnetri	$$⊢A\ne C$$

Proof

Step	Hyp	Ref	Expression
1		eqnetr.1	$$⊢A=B$$
2		eqnetr.2	$$⊢B\ne C$$
3	1	neeq1i	$$⊢A\ne C\leftrightarrow B\ne C$$
4	2 3	mpbir	$$⊢A\ne C$$