Theorem 3netr4g

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

	Ref	Expression
Hypotheses	3netr4g.1	|- ( ph -> A =/= B )
	3netr4g.2	|- C = A
	3netr4g.3	|- D = B
Assertion	3netr4g	|- ( ph -> C =/= D )

Proof

Step	Hyp	Ref	Expression
1		3netr4g.1	|- ( ph -> A =/= B )
2		3netr4g.2	|- C = A
3		3netr4g.3	|- D = B
4	2 3	neeq12i	|- ( C =/= D <-> A =/= B )
5	1 4	sylibr	|- ( ph -> C =/= D )