Theorem neeqtrrd

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

	Ref	Expression
Hypotheses	neeqtrrd.1	$$⊢\phi \to A\ne B$$
	neeqtrrd.2	$$⊢\phi \to C=B$$
Assertion	neeqtrrd	$$⊢\phi \to A\ne C$$

Proof

Step	Hyp	Ref	Expression
1		neeqtrrd.1	$$⊢\phi \to A\ne B$$
2		neeqtrrd.2	$$⊢\phi \to C=B$$
3	2	eqcomd	$$⊢\phi \to B=C$$
4	1 3	neeqtrd	$$⊢\phi \to A\ne C$$