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	$$⊢\phi \to B\ne C$$
Assertion	eqnetrrid	$$⊢\phi \to A\ne C$$

Proof

Step	Hyp	Ref	Expression
1		eqnetrrid.1	$$⊢B=A$$
2		eqnetrrid.2	$$⊢\phi \to B\ne C$$
3	1	a1i	$$⊢\phi \to B=A$$
4	3 2	eqnetrrd	$$⊢\phi \to A\ne C$$