Theorem difid

Description: The difference between a class and itself is the empty set. Proposition 5.15 of TakeutiZaring p. 20. Also Theorem 32 of Suppes p. 28. (Contributed by NM, 22-Apr-2004)

	Ref	Expression
Assertion	difid	$$⊢A\setminus A=\varnothing$$

Proof

Step	Hyp	Ref	Expression
1		ssid	$$⊢A\subseteq A$$
2		ssdif0	$$⊢A\subseteq A\leftrightarrow A\setminus A=\varnothing$$
3	1 2	mpbi	$$⊢A\setminus A=\varnothing$$