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Metamath Proof Explorer

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