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

Metamath Proof Explorer

Theorem 0ima

Description: Image under the empty relation. (Contributed by FL, 11-Jan-2007)

		Ref	Expression
	Assertion	0ima	$⊢ \emptyset [A] = \emptyset$

Step	Hyp	Ref	Expression
1		imassrn	$⊢ \emptyset [A] \subseteq ran \emptyset$
2		rn0	$⊢ ran \emptyset = \emptyset$
3	1 2	sseqtri	$⊢ \emptyset [A] \subseteq \emptyset$
4		0ss	$⊢ \emptyset \subseteq \emptyset [A]$
5	3 4	eqssi	$⊢ \emptyset [A] = \emptyset$