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Theorem iota2df 5556
 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 459 . . . 4
43eqeq2d 2416 . . 3
52, 4bibi12d 319 . 2
6 iota2df.2 . . 3
7 iota1 5546 . . 3
86, 7syl 17 . 2
9 iota2df.4 . 2
10 iota2df.6 . 2
11 iota2df.5 . . 3
12 nfiota1 5534 . . . . 5
1312a1i 11 . . . 4
1413, 10nfeqd 2571 . . 3
1511, 14nfbid 1961 . 2
161, 5, 8, 9, 10, 15vtocldf 3107 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 367   wceq 1405  wnf 1637   wcel 1842  weu 2238  wnfc 2550  cio 5530 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 976  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-eu 2242  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ral 2758  df-rex 2759  df-v 3060  df-sbc 3277  df-un 3418  df-sn 3972  df-pr 3974  df-uni 4191  df-iota 5532 This theorem is referenced by:  iota2d  5557  iota2  5558  riota2df  6259  opiota  6842
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