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	$$⊢A\in B\to A\subseteq \bigcup B$$

Proof

Step	Hyp	Ref	Expression
1		ssid	$$⊢A\subseteq A$$
2		ssuni	$$⊢\left(A\subseteq A\wedge A\in B\right)\to A\subseteq \bigcup B$$
3	1 2	mpan	$$⊢A\in B\to A\subseteq \bigcup B$$