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Theorem iunxsn 3733
 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 3732 . 2
41, 3ax-mp 7 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1243   wcel 1393  cvv 2557  csn 3375  ciun 3657 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-sbc 2765  df-sn 3381  df-iun 3659 This theorem is referenced by:  iunsuc  4157
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