Theorem ustne0

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

	Ref	Expression
Assertion	ustne0	⊢ ( 𝑈 ∈ ( UnifOn ‘ 𝑋 ) → 𝑈 ≠ ∅ )

Proof

Step	Hyp	Ref	Expression
1		ustbasel	⊢ ( 𝑈 ∈ ( UnifOn ‘ 𝑋 ) → ( 𝑋 × 𝑋 ) ∈ 𝑈 )
2	1	ne0d	⊢ ( 𝑈 ∈ ( UnifOn ‘ 𝑋 ) → 𝑈 ≠ ∅ )