Theorem eqnetrrid

Description: A chained equality inference for inequality. (Contributed by NM, 6-Jun-2012) (Proof shortened by Wolf Lammen, 19-Nov-2019)

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

Proof

Step	Hyp	Ref	Expression
1		eqnetrrid.1	|- B = A
2		eqnetrrid.2	|- ( ph -> B =/= C )
3	1	a1i	|- ( ph -> B = A )
4	3 2	eqnetrrd	|- ( ph -> A =/= C )