Theorem eqnetrrd

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

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

Proof

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