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Theorem iunxsng 3854
 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 3783 . . 3
2 iunxsng.1 . . . . 5
32eleq2d 2184 . . . 4
43rexsng 3531 . . 3
51, 4syl5bb 191 . 2
65eqrdv 2113 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1314   wcel 1463  wrex 2391  csn 3493  ciun 3779 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-3an 947  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2244  df-ral 2395  df-rex 2396  df-v 2659  df-sbc 2879  df-sn 3499  df-iun 3781 This theorem is referenced by:  iunxsn  3855  iunxprg  3859  rdgisuc1  6235  oasuc  6314  omsuc  6322
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