Theorem unidm 2178

Description: Idempotent law for union of classes. Theorem 23 of [Suppes] p. 27.

Assertion

Ref	Expression
unidm	⊢ (A ∪ A) = A

Proof of Theorem unidm

Step	Hyp	Ref	Expression
1		oridm 243	. 2 ⊢ ((x ∈ A ⋁ x ∈ A) ↔ x ∈ A)
2	1	uneqri 2177	1 ⊢ (A ∪ A) = A

Syntax hints:   = wceq 958   ∈ wcel 960   ∪ cun 2048

This theorem is referenced by:  unundi 2194  unundir 2195  uneqin 2259  dfsn2 2424  unisn 2521  mapunen 4508  pm54.43 4581  inposet 10477

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-v 1815  df-un 2053

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