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Theorem iunxsng 4162
 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 4090 . . 3
2 iunxsng.1 . . . . 5
32eleq2d 2503 . . . 4
43rexsng 3840 . . 3
51, 4syl5bb 249 . 2
65eqrdv 2434 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  wrex 2699  csn 3807  ciun 4086 This theorem is referenced by:  iunxsn  4163  iunxprg  28059 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2703  df-rex 2704  df-v 2951  df-sbc 3155  df-sn 3813  df-iun 4088
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