Theorem 3netr3d

Description: Substitution of equality into both sides of an inequality. (Contributed by NM, 24-Jul-2012) (Proof shortened by Wolf Lammen, 19-Nov-2019)

	Ref	Expression
Hypotheses	3netr3d.1	|- ( ph -> A =/= B )
	3netr3d.2	|- ( ph -> A = C )
	3netr3d.3	|- ( ph -> B = D )
Assertion	3netr3d	|- ( ph -> C =/= D )

Proof

Step	Hyp	Ref	Expression
1		3netr3d.1	|- ( ph -> A =/= B )
2		3netr3d.2	|- ( ph -> A = C )
3		3netr3d.3	|- ( ph -> B = D )
4	1 3	neeqtrd	|- ( ph -> A =/= D )
5	2 4	eqnetrrd	|- ( ph -> C =/= D )