Metamath Proof Explorer


Theorem unexb

Description: Existence of union is equivalent to existence of its components. (Contributed by NM, 11-Jun-1998)

Ref Expression
Assertion unexb A V B V A B V

Proof

Step Hyp Ref Expression
1 unexg A V B V A B V
2 ssun1 A A B
3 ssexg A A B A B V A V
4 2 3 mpan A B V A V
5 ssun2 B A B
6 ssexg B A B A B V B V
7 5 6 mpan A B V B V
8 4 7 jca A B V A V B V
9 1 8 impbii A V B V A B V