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Theorem iunxsng 4359
 Description: A singleton index picks out an instance of an indexed union's argument. (Contributed by Mario Carneiro, 25-Jun-2016.)
Hypothesis
Ref Expression
iunxsng.1
Assertion
Ref Expression
iunxsng
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem iunxsng
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eliun 4282 . . 3
2 iunxsng.1 . . . . 5
32eleq2d 2513 . . . 4
43rexsng 4006 . . 3
51, 4syl5bb 261 . 2
65eqrdv 2448 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1443   wcel 1886  wrex 2737  csn 3967  ciun 4277 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-10 1914  ax-11 1919  ax-12 1932  ax-13 2090  ax-ext 2430 This theorem depends on definitions:  df-bi 189  df-an 373  df-3an 986  df-tru 1446  df-ex 1663  df-nf 1667  df-sb 1797  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2580  df-ral 2741  df-rex 2742  df-v 3046  df-sbc 3267  df-sn 3968  df-iun 4279 This theorem is referenced by:  iunxsn  4360  disjiun2  37392  carageniuncllem1  38336  caratheodorylem1  38341  iunxprg  38998
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