Theorem unisn

Description: A set equals the union of its singleton. Theorem 8.2 of Quine p. 53. (Contributed by NM, 30-Aug-1993)

	Ref	Expression
Hypothesis	unisn.1	⊢ 𝐴 ∈ V
Assertion	unisn	⊢ ∪ { 𝐴 } = 𝐴

Proof

Step	Hyp	Ref	Expression
1		unisn.1	⊢ 𝐴 ∈ V
2		unisng	⊢ ( 𝐴 ∈ V → ∪ { 𝐴 } = 𝐴 )
3	1 2	ax-mp	⊢ ∪ { 𝐴 } = 𝐴