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Theorem iotaval 6154
 Description: Theorem 8.19 in [Quine] p. 57. This theorem is the fundamental property of iota. (Contributed by Andrew Salmon, 11-Jul-2011.)
Assertion
Ref Expression
iotaval
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem iotaval
StepHypRef Expression
1 dfiota2 6144 . 2
2 vex 2730 . . . . . . 7
3 sbeqalb 2973 . . . . . . . 8
4 equcomi 1822 . . . . . . . 8
53, 4syl6 31 . . . . . . 7
62, 5ax-mp 10 . . . . . 6
76ex 425 . . . . 5
8 equequ2 1830 . . . . . . . . . 10
98eqcoms 2256 . . . . . . . . 9
109bibi2d 311 . . . . . . . 8
1110biimpd 200 . . . . . . 7
1211alimdv 2017 . . . . . 6
1312com12 29 . . . . 5
147, 13impbid 185 . . . 4
1514alrimiv 2012 . . 3
16 uniabio 6153 . . 3
1715, 16syl 17 . 2
181, 17syl5eq 2297 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wa 360  wal 1532   wceq 1619   wcel 1621  cab 2239  cvv 2727  cuni 3727  cio 6141 This theorem is referenced by:  iotauni  6155  iota1  6157  iotaex  6160  iota4  6161  iota5  6163  iotain  26784  iotaexeu  26785  iotasbc  26786  iotaequ  26796  iotavalb  26797  pm14.24  26799  sbiota1  26801 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-v 2729  df-sbc 2922  df-un 3083  df-sn 3550  df-pr 3551  df-uni 3728  df-iota 6143
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