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Theorem iota2df 5434
 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 448 . . . 4
43eqeq2d 2446 . . 3
52, 4bibi12d 313 . 2
6 iota2df.2 . . 3
7 iota1 5424 . . 3
86, 7syl 16 . 2
9 iota2df.4 . 2
10 iota2df.6 . 2
11 iota2df.5 . . 3
12 nfiota1 5412 . . . . 5
1312a1i 11 . . . 4
1413, 10nfeqd 2585 . . 3
1511, 14nfbid 1854 . 2
161, 5, 8, 9, 10, 15vtocldf 2995 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wnf 1553   wceq 1652   wcel 1725  weu 2280  wnfc 2558  cio 5408 This theorem is referenced by:  iota2d  5435  iota2  5436  opiota  6527  riota2df  6562 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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