Theorem necon3bii

Description: Inference from equality to inequality. (Contributed by NM, 23-Feb-2005)

	Ref	Expression
Hypothesis	necon3bii.1	$$⊢A=B\leftrightarrow C=D$$
Assertion	necon3bii	$$⊢A\ne B\leftrightarrow C\ne D$$

Proof

Step	Hyp	Ref	Expression
1		necon3bii.1	$$⊢A=B\leftrightarrow C=D$$
2	1	necon3abii	$$⊢A\ne B\leftrightarrow \neg C=D$$
3		df-ne	$$⊢C\ne D\leftrightarrow \neg C=D$$
4	2 3	bitr4i	$$⊢A\ne B\leftrightarrow C\ne D$$