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Theorem iunxsng 4044
 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 3973 . . 3
2 iunxsng.1 . . . . 5
32eleq2d 2420 . . . 4
43rexsng 3766 . . 3
51, 4syl5bb 248 . 2
65eqrdv 2351 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1642   wcel 1710  wrex 2615  csn 3737  ciun 3969 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-3an 936  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-ral 2619  df-rex 2620  df-v 2861  df-sbc 3047  df-sn 3741  df-iun 3971 This theorem is referenced by:  iunxsn  4045
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