Theorem neeq2d

Description: Deduction for inequality. (Contributed by NM, 25-Oct-1999) (Proof shortened by Wolf Lammen, 19-Nov-2019)

	Ref	Expression
Hypothesis	neeq1d.1	$$⊢\phi \to A=B$$
Assertion	neeq2d	$$⊢\phi \to \left(C\ne A\leftrightarrow C\ne B\right)$$

Proof

Step	Hyp	Ref	Expression
1		neeq1d.1	$$⊢\phi \to A=B$$
2	1	eqeq2d	$$⊢\phi \to \left(C=A\leftrightarrow C=B\right)$$
3	2	necon3bid	$$⊢\phi \to \left(C\ne A\leftrightarrow C\ne B\right)$$