Theorem eqnetrd

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

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

Proof

Step	Hyp	Ref	Expression
1		eqnetrd.1	|- ( ph -> A = B )
2		eqnetrd.2	|- ( ph -> B =/= C )
3	1	neeq1d	|- ( ph -> ( A =/= C <-> B =/= C ) )
4	2 3	mpbird	|- ( ph -> A =/= C )