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Theorem unidm 3407
 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 500 . 2 ((x A x A) ↔ x A)
21uneqri 3406 1 (AA) = A
 Colors of variables: wff setvar class Syntax hints:   = wceq 1642   ∈ wcel 1710   ∪ cun 3207 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-un 3214 This theorem is referenced by:  unundi  3424  unundir  3425  uneqin  3506  difabs  3518  undifabs  3627  dfif5  3674  dfsn2  3747  diftpsn3  3849  unisn  3907
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