This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

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	$⊢ A ∖ A = \emptyset$

Proof

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