Theorem unidm

Description: Idempotent law for union of classes. Theorem 23 of Suppes p. 27. (Contributed by NM, 21-Jun-1993)

	Ref	Expression
Assertion	unidm	⊢ ( 𝐴 ∪ 𝐴 ) = 𝐴

Proof

Step	Hyp	Ref	Expression
1		oridm	⊢ ( ( 𝑥 ∈ 𝐴 ∨ 𝑥 ∈ 𝐴 ) ↔ 𝑥 ∈ 𝐴 )
2	1	uneqri	⊢ ( 𝐴 ∪ 𝐴 ) = 𝐴