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Theorem iotasbc 26786
 Description: Definition *14.01 in [WhiteheadRussell] p. 184. In Principia Mathematica, Russell and Whitehead define in terms of a function of . Their definition differs in that a function of evaluates to "false" when there isn't a single that satisfies . (Contributed by Andrew Salmon, 11-Jul-2011.)
Assertion
Ref Expression
iotasbc
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   (,)

Proof of Theorem iotasbc
StepHypRef Expression
1 sbc5 2945 . 2
2 iotaexeu 26785 . . . . . . 7
3 eueq 2874 . . . . . . 7
42, 3sylib 190 . . . . . 6
5 df-eu 2118 . . . . . . 7
6 iotaval 6154 . . . . . . . . . 10
76eqcomd 2258 . . . . . . . . 9
87ancri 537 . . . . . . . 8
98eximi 1574 . . . . . . 7
105, 9sylbi 189 . . . . . 6
11 eupick 2176 . . . . . 6
124, 10, 11syl2anc 645 . . . . 5
1312, 7impbid1 196 . . . 4
1413anbi1d 688 . . 3
1514exbidv 2005 . 2
161, 15syl5bb 250 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wa 360  wal 1532  wex 1537   wceq 1619   wcel 1621  weu 2114  cvv 2727  wsbc 2921  cio 6141 This theorem is referenced by:  iotasbc2  26787  iotavalb  26797  fvsb  26822 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-eu 2118  df-mo 2119  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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