Theorem brvdif

Description: Binary relation with universal complement is the negation of the relation. (Contributed by Peter Mazsa, 1-Jul-2018)

	Ref	Expression
Assertion	brvdif	$$⊢A\left(\mathrm{V}\setminus R\right)B\leftrightarrow \neg ARB$$

Proof

Step	Hyp	Ref	Expression
1		brv	$$⊢A\mathrm{V}B$$
2		brdif	$$⊢A\left(\mathrm{V}\setminus R\right)B\leftrightarrow \left(A\mathrm{V}B\wedge \neg ARB\right)$$
3	1 2	mpbiran	$$⊢A\left(\mathrm{V}\setminus R\right)B\leftrightarrow \neg ARB$$