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Theorem dfiota2 6144
 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 6143 . 2
2 df-sn 3550 . . . . . 6
32eqeq2i 2263 . . . . 5
4 abbi 2359 . . . . 5
53, 4bitr4i 245 . . . 4
65abbii 2361 . . 3
76unieqi 3737 . 2
81, 7eqtri 2273 1
 Colors of variables: wff set class Syntax hints:   wb 178  wal 1532   wceq 1619  cab 2239  csn 3544  cuni 3727  cio 6141 This theorem is referenced by:  nfiota1  6145  nfiotad  6146  cbviota  6148  sb8iota  6150  iotaval  6154  iotanul  6158  fv4  6172 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-rex 2514  df-sn 3550  df-uni 3728  df-iota 6143
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