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Theorem iota2df 5580
 Description: A condition that allows us to represent "the unique element such that " with a class expression . (Contributed by NM, 30-Dec-2014.)
Hypotheses
Ref Expression
iota2df.1
iota2df.2
iota2df.3
iota2df.4
iota2df.5
iota2df.6
Assertion
Ref Expression
iota2df

Proof of Theorem iota2df
StepHypRef Expression
1 iota2df.1 . 2
2 iota2df.3 . . 3
3 simpr 461 . . . 4
43eqeq2d 2471 . . 3
52, 4bibi12d 321 . 2
6 iota2df.2 . . 3
7 iota1 5570 . . 3
86, 7syl 16 . 2
9 iota2df.4 . 2
10 iota2df.6 . 2
11 iota2df.5 . . 3
12 nfiota1 5558 . . . . 5
1312a1i 11 . . . 4
1413, 10nfeqd 2626 . . 3
1511, 14nfbid 1933 . 2
161, 5, 8, 9, 10, 15vtocldf 3158 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  F/wnf 1616  e.wcel 1818  E!weu 2282  F/_wnfc 2605  iotacio 5554 This theorem is referenced by:  iota2d  5581  iota2  5582  riota2df  6278  opiota  6859 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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