Theorem unveldom

Description: The universe is an element of the domain of the probability, the universe (entire probability space) being U. dom P in our construction. (Contributed by Thierry Arnoux, 22-Jan-2017)

	Ref	Expression
Assertion	unveldom	⊢ ( 𝑃 ∈ Prob → ∪ dom 𝑃 ∈ dom 𝑃 )

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( 𝑃 ∈ Prob → 𝑃 ∈ Prob )
2	1	unveldomd	⊢ ( 𝑃 ∈ Prob → ∪ dom 𝑃 ∈ dom 𝑃 )