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Theorem iotasbc 36840
 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 3280 . 2
2 iotaexeu 36839 . . . . . . 7
3 eueq 3198 . . . . . . 7
42, 3sylib 201 . . . . . 6
5 df-eu 2323 . . . . . . 7
6 iotaval 5564 . . . . . . . . . 10
76eqcomd 2477 . . . . . . . . 9
87ancri 561 . . . . . . . 8
98eximi 1715 . . . . . . 7
105, 9sylbi 200 . . . . . 6
11 eupick 2385 . . . . . 6
124, 10, 11syl2anc 673 . . . . 5
1312, 7impbid1 208 . . . 4
1413anbi1d 719 . . 3
1514exbidv 1776 . 2
161, 15syl5bb 265 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189   wa 376  wal 1450   wceq 1452  wex 1671   wcel 1904  weu 2319  cvv 3031  wsbc 3255  cio 5551 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-mo 2324  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-rex 2762  df-v 3033  df-sbc 3256  df-un 3395  df-sn 3960  df-pr 3962  df-uni 4191  df-iota 5553 This theorem is referenced by:  iotasbc2  36841  iotavalb  36851  fvsb  36875
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