Theorem 3netr3g

Description: Substitution of equality into both sides of an inequality. (Contributed by NM, 24-Jul-2012)

	Ref	Expression
Hypotheses	3netr3g.1	$$⊢\phi \to A\ne B$$
	3netr3g.2	$$⊢A=C$$
	3netr3g.3	$$⊢B=D$$
Assertion	3netr3g	$$⊢\phi \to C\ne D$$

Proof

Step	Hyp	Ref	Expression
1		3netr3g.1	$$⊢\phi \to A\ne B$$
2		3netr3g.2	$$⊢A=C$$
3		3netr3g.3	$$⊢B=D$$
4	2 3	neeq12i	$$⊢A\ne B\leftrightarrow C\ne D$$
5	1 4	sylib	$$⊢\phi \to C\ne D$$