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Theorem iota1 4881
 Description: Property of iota. (Contributed by NM, 23-Aug-2011.) (Revised by Mario Carneiro, 23-Dec-2016.)
Assertion
Ref Expression
iota1

Proof of Theorem iota1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-eu 1903 . 2
2 sp 1401 . . . . 5
3 iotaval 4878 . . . . . 6
43eqeq2d 2051 . . . . 5
52, 4bitr4d 180 . . . 4
6 eqcom 2042 . . . 4
75, 6syl6bb 185 . . 3
87exlimiv 1489 . 2
91, 8sylbi 114 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98  wal 1241   wceq 1243  wex 1381  weu 1900  cio 4865 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-rex 2312  df-v 2559  df-sbc 2765  df-un 2922  df-sn 3381  df-pr 3382  df-uni 3581  df-iota 4867 This theorem is referenced by:  iota2df  4891  sniota  4894  tz6.12-1  5200  riota1  5486  riota1a  5487  erovlem  6198
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