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 \ A ) = (/)

Proof

Step	Hyp	Ref	Expression
1		ssid	|- A C_ A
2		ssdif0	|- ( A C_ A <-> ( A \ A ) = (/) )
3	1 2	mpbi	|- ( A \ A ) = (/)