Theorem neeqtrd

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

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

Proof

Step	Hyp	Ref	Expression
1		neeqtrd.1	|- ( ph -> A =/= B )
2		neeqtrd.2	|- ( ph -> B = C )
3	2	neeq2d	|- ( ph -> ( A =/= B <-> A =/= C ) )
4	1 3	mpbid	|- ( ph -> A =/= C )