Theorem ustne0

Description: A uniform structure cannot be empty. (Contributed by Thierry Arnoux, 16-Nov-2017)

	Ref	Expression
Assertion	ustne0	$$⊢U\in \mathrm{UnifOn}\left(X\right)\to U\ne \varnothing$$

Proof

Step	Hyp	Ref	Expression
1		ustbasel	$$⊢U\in \mathrm{UnifOn}\left(X\right)\to X\times X\in U$$
2	1	ne0d	$$⊢U\in \mathrm{UnifOn}\left(X\right)\to U\ne \varnothing$$