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 ⊆ 𝐴
2		ssdif0	⊢ ( 𝐴 ⊆ 𝐴 ↔ ( 𝐴 ∖ 𝐴 ) = ∅ )
3	1 2	mpbi	⊢ ( 𝐴 ∖ 𝐴 ) = ∅