Metamath Proof Explorer

Theorem elssuni

Description: An element of a class is a subclass of its union. Theorem 8.6 of Quine p. 54. Also the basis for Proposition 7.20 of TakeutiZaring p. 40. (Contributed by NM, 6-Jun-1994)

Ref Expression
Assertion elssuni A B A B


Step Hyp Ref Expression
1 ssid A A
2 ssuni A A A B A B
3 1 2 mpan A B A B