Theorem 3netr4g

Description: Substitution of equality into both sides of an inequality. (Contributed by NM, 14-Jun-2012)

	Ref	Expression
Hypotheses	3netr4g.1	$$⊢\phi \to A\ne B$$
	3netr4g.2	$$⊢C=A$$
	3netr4g.3	$$⊢D=B$$
Assertion	3netr4g	$$⊢\phi \to C\ne D$$

Proof

Step	Hyp	Ref	Expression
1		3netr4g.1	$$⊢\phi \to A\ne B$$
2		3netr4g.2	$$⊢C=A$$
3		3netr4g.3	$$⊢D=B$$
4	2 3	neeq12i	$$⊢C\ne D\leftrightarrow A\ne B$$
5	1 4	sylibr	$$⊢\phi \to C\ne D$$