Theorem neeqtrrd

Description: Substitution of equal classes into an inequality. (Contributed by NM, 4-Jul-2012)

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

Proof

Step	Hyp	Ref	Expression
1		neeqtrrd.1	|- ( ph -> A =/= B )
2		neeqtrrd.2	|- ( ph -> C = B )
3	2	eqcomd	|- ( ph -> B = C )
4	1 3	neeqtrd	|- ( ph -> A =/= C )