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Theorem iunxsng 4409
 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:   ,   ,

Proof of Theorem iunxsng
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eliun 4335 . . 3
2 iunxsng.1 . . . . 5
32eleq2d 2527 . . . 4
43rexsng 4065 . . 3
51, 4syl5bb 257 . 2
65eqrdv 2454 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  =wceq 1395  e.wcel 1818  E.wrex 2808  {csn 4029  U_ciun 4330 This theorem is referenced by:  iunxsn  4410  iunxprg  32302 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-v 3111  df-sbc 3328  df-sn 4030  df-iun 4332
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