Theorem difidALT

Description: Alternate proof of difid . Shorter, but requiring ax-8 , df-clel . (Contributed by NM, 22-Apr-2004) (Proof modification is discouraged.) (New usage is discouraged.)

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

Proof

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