Theorem difabs

Description: Absorption-like law for class difference: you can remove a class only once. (Contributed by FL, 2-Aug-2009)

	Ref	Expression
Assertion	difabs	$$⊢\left(A\setminus B\right)\setminus B=A\setminus B$$

Proof

Step	Hyp	Ref	Expression
1		difun1	$$⊢A\setminus \left(B\cup B\right)=\left(A\setminus B\right)\setminus B$$
2		unidm	$$⊢B\cup B=B$$
3	2	difeq2i	$$⊢A\setminus \left(B\cup B\right)=A\setminus B$$
4	1 3	eqtr3i	$$⊢\left(A\setminus B\right)\setminus B=A\setminus B$$