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Theorem iota2 5436
 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:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem iota2
StepHypRef Expression
1 elex 2956 . 2
2 simpl 444 . . 3
3 simpr 448 . . 3
4 iota2.1 . . . 4
54adantl 453 . . 3
6 nfv 1629 . . . 4
7 nfeu1 2290 . . . 4
86, 7nfan 1846 . . 3
9 nfvd 1630 . . 3
10 nfcvd 2572 . . 3
112, 3, 5, 8, 9, 10iota2df 5434 . 2
121, 11sylan 458 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wceq 1652   wcel 1725  weu 2280  cvv 2948  cio 5408 This theorem is referenced by:  pczpre  13213  pcdiv  13218  unirep  26405 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-v 2950  df-sbc 3154  df-un 3317  df-sn 3812  df-pr 3813  df-uni 4008  df-iota 5410
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