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Theorem uniintabim 3652
 Description: The union and the intersection of a class abstraction are equal if there is a unique satisfying value of . (Contributed by Jim Kingdon, 14-Aug-2018.)
Assertion
Ref Expression
uniintabim

Proof of Theorem uniintabim
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 euabsn2 3439 . 2
2 uniintsnr 3651 . 2
31, 2sylbi 114 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1243  wex 1381  weu 1900  cab 2026  csn 3375  cuni 3580  cint 3615 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-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-un 2922  df-in 2924  df-sn 3381  df-pr 3382  df-uni 3581  df-int 3616 This theorem is referenced by:  iotaint  4880
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