Theorem 3netr4d

Description: Substitution of equality into both sides of an inequality. (Contributed by NM, 24-Jul-2012) (Proof shortened by Wolf Lammen, 21-Nov-2019)

	Ref	Expression
Hypotheses	3netr4d.1	|- ( ph -> A =/= B )
	3netr4d.2	|- ( ph -> C = A )
	3netr4d.3	|- ( ph -> D = B )
Assertion	3netr4d	|- ( ph -> C =/= D )

Proof

Step	Hyp	Ref	Expression
1		3netr4d.1	|- ( ph -> A =/= B )
2		3netr4d.2	|- ( ph -> C = A )
3		3netr4d.3	|- ( ph -> D = B )
4	2 1	eqnetrd	|- ( ph -> C =/= B )
5	4 3	neeqtrrd	|- ( ph -> C =/= D )