Theorem un0

Description: The union of a class with the empty set is itself. Dual of inv1 . Commuted form of 0un . Theorem 24 of Suppes p. 27. (Contributed by NM, 15-Jul-1993)

	Ref	Expression
Assertion	un0	$$⊢A\cup \varnothing =A$$

Proof

Step	Hyp	Ref	Expression
1		noel	$$⊢\neg x\in \varnothing$$
2	1	biorfri	$$⊢x\in A\leftrightarrow \left(x\in A\vee x\in \varnothing \right)$$
3	2	bicomi	$$⊢\left(x\in A\vee x\in \varnothing \right)\leftrightarrow x\in A$$
4	3	uneqri	$$⊢A\cup \varnothing =A$$