Theorem neneqd

Description: Deduction eliminating inequality definition. (Contributed by Jonathan Ben-Naim, 3-Jun-2011)

	Ref	Expression
Hypothesis	neneqd.1	$$⊢\phi \to A\ne B$$
Assertion	neneqd	$$⊢\phi \to \neg A=B$$

Proof

Step	Hyp	Ref	Expression
1		neneqd.1	$$⊢\phi \to A\ne B$$
2		df-ne	$$⊢A\ne B\leftrightarrow \neg A=B$$
3	1 2	sylib	$$⊢\phi \to \neg A=B$$