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Theorem dfiota2 5089
 Description: Alternate definition for descriptions. Definition 8.18 in [Quine] p. 56. (Contributed by Andrew Salmon, 30-Jun-2011.)
Assertion
Ref Expression
dfiota2
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem dfiota2
StepHypRef Expression
1 df-iota 5088 . 2
2 df-sn 3533 . . . . . 6
32eqeq2i 2150 . . . . 5
4 abbi 2253 . . . . 5
53, 4bitr4i 186 . . . 4
65abbii 2255 . . 3
76unieqi 3746 . 2
81, 7eqtri 2160 1
 Colors of variables: wff set class Syntax hints:   wb 104  wal 1329   wceq 1331  cab 2125  csn 3527  cuni 3736  cio 5086 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-rex 2422  df-sn 3533  df-uni 3737  df-iota 5088 This theorem is referenced by:  nfiota1  5090  nfiotadw  5091  cbviota  5093  sb8iota  5095  iotaval  5099  iotanul  5103  fv2  5416
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