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Theorem uniabio 4823
Description: Part of Theorem 8.17 in [Quine] p. 56. This theorem serves as a lemma for the fundamental property of iota. (Contributed by Andrew Salmon, 11-Jul-2011.)
Assertion
Ref Expression
uniabio  U. {  |  }
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem uniabio
StepHypRef Expression
1 abbi 2151 . . . . 5  {  |  }  {  |  }
21biimpi 113 . . . 4  {  |  }  {  |  }
3 df-sn 3376 . . . 4  { }  {  |  }
42, 3syl6eqr 2090 . . 3  {  |  }  { }
54unieqd 3585 . 2  U. {  |  }  U. { }
6 vex 2557 . . 3 
_V
76unisn 3590 . 2  U. { }
85, 7syl6eq 2088 1  U. {  |  }
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98  wal 1241   wceq 1243   {cab 2026   {csn 3370   U.cuni 3574
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-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2309  df-v 2556  df-un 2919  df-sn 3376  df-pr 3377  df-uni 3575
This theorem is referenced by:  iotaval  4824  iotauni  4825
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