Theorem 0ima

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

	Ref	Expression
Assertion	0ima	$$⊢\varnothing \left[A\right]=\varnothing$$

Proof

Step	Hyp	Ref	Expression
1		imassrn	$$⊢\varnothing \left[A\right]\subseteq \mathrm{ran}\varnothing$$
2		rn0	$$⊢\mathrm{ran}\varnothing =\varnothing$$
3	1 2	sseqtri	$$⊢\varnothing \left[A\right]\subseteq \varnothing$$
4		0ss	$$⊢\varnothing \subseteq \varnothing \left[A\right]$$
5	3 4	eqssi	$$⊢\varnothing \left[A\right]=\varnothing$$