Theorem 3netr3g

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

	Ref	Expression
Hypotheses	3netr3g.1	|- ( ph -> A =/= B )
	3netr3g.2	|- A = C
	3netr3g.3	|- B = D
Assertion	3netr3g	|- ( ph -> C =/= D )

Proof

Step	Hyp	Ref	Expression
1		3netr3g.1	|- ( ph -> A =/= B )
2		3netr3g.2	|- A = C
3		3netr3g.3	|- B = D
4	2 3	neeq12i	|- ( A =/= B <-> C =/= D )
5	1 4	sylib	|- ( ph -> C =/= D )