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Theorem unidm 3222
 Description: Idempotent law for union of classes. Theorem 23 of [Suppes] p. 27. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
unidm (𝐴𝐴) = 𝐴

Proof of Theorem unidm
Dummy variable 𝑥 is distinct from all other variables.
StepHypRef Expression
1 oridm 747 . 2 ((𝑥𝐴𝑥𝐴) ↔ 𝑥𝐴)
21uneqri 3221 1 (𝐴𝐴) = 𝐴
 Colors of variables: wff set class Syntax hints:   = wceq 1332   ∈ wcel 1481   ∪ cun 3072 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2691  df-un 3078 This theorem is referenced by:  unundi  3240  unundir  3241  uneqin  3330  difabs  3343  dfsn2  3544  diftpsn3  3667  unisn  3758  dfdm2  5079  fun2  5302  resasplitss  5308  xpider  6506  pm54.43  7061
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