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Theorem euiotaex 4826
Description: Theorem 8.23 in [Quine] p. 58, with existential uniqueness condition added. This theorem proves the existence of the  iota class under our definition. (Contributed by Jim Kingdon, 21-Dec-2018.)
Assertion
Ref Expression
euiotaex  iota 
_V

Proof of Theorem euiotaex
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 iotaval 4821 . . . 4  iota
21eqcomd 2042 . . 3  iota
32eximi 1488 . 2  iota
4 df-eu 1900 . 2
5 isset 2555 . 2 
iota 
_V  iota
63, 4, 53imtr4i 190 1  iota 
_V
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98  wal 1240   wceq 1242  wex 1378   wcel 1390  weu 1897   _Vcvv 2551   iotacio 4808
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-eu 1900  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-v 2553  df-sbc 2759  df-un 2916  df-sn 3373  df-pr 3374  df-uni 3572  df-iota 4810
This theorem is referenced by:  iota4an  4829  funfvex  5135
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