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Theorem iota2 5582
 Description: The unique element such that . (Contributed by Jeff Madsen, 1-Jun-2011.) (Revised by Mario Carneiro, 23-Dec-2016.)
Hypothesis
Ref Expression
iota2.1
Assertion
Ref Expression
iota2
Distinct variable groups:   ,   ,

Proof of Theorem iota2
StepHypRef Expression
1 elex 3118 . 2
2 simpl 457 . . 3
3 simpr 461 . . 3
4 iota2.1 . . . 4
54adantl 466 . . 3
6 nfv 1707 . . . 4
7 nfeu1 2294 . . . 4
86, 7nfan 1928 . . 3
9 nfvd 1708 . . 3
10 nfcvd 2620 . . 3
112, 3, 5, 8, 9, 10iota2df 5580 . 2
121, 11sylan 471 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  E!weu 2282   cvv 3109  iotacio 5554 This theorem is referenced by:  pczpre  14371  pcdiv  14376  rngurd  27778  unirep  30203  ellimciota  31620  bj-nuliota  34586 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-v 3111  df-sbc 3328  df-un 3480  df-sn 4030  df-pr 4032  df-uni 4250  df-iota 5556
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