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Theorem iunxsn 4045
 Description: A singleton index picks out an instance of an indexed union's argument. (Contributed by NM, 26-Mar-2004.) (Proof shortened by Mario Carneiro, 25-Jun-2016.)
Hypotheses
Ref Expression
iunxsn.1
iunxsn.2
Assertion
Ref Expression
iunxsn
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem iunxsn
StepHypRef Expression
1 iunxsn.1 . 2
2 iunxsn.2 . . 3
32iunxsng 4044 . 2
41, 3ax-mp 5 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1642   wcel 1710  cvv 2859  csn 3737  ciun 3969 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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: (None)
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