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Theorem iota2df 5259
 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.6 . 2
2 iota2df.5 . . 3
3 nfiota1 5237 . . . . 5
43a1i 10 . . . 4
54, 1nfeqd 2446 . . 3
62, 5nfbid 1774 . 2
7 iota2df.4 . . 3
8 iota2df.3 . . . . 5
9 simpr 447 . . . . . 6
109eqeq2d 2307 . . . . 5
118, 10bibi12d 312 . . . 4
1211ex 423 . . 3
137, 12alrimi 1757 . 2
14 iota2df.2 . . . 4
15 iota1 5249 . . . 4
1614, 15syl 15 . . 3
177, 16alrimi 1757 . 2
18 iota2df.1 . 2
19 vtoclgft 2847 . 2
201, 6, 13, 17, 18, 19syl221anc 1193 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wal 1530  wnf 1534   wceq 1632   wcel 1696  weu 2156  wnfc 2419  cio 5233 This theorem is referenced by:  iota2d  5260  iota2  5261  opiota  6306  riota2df  6341 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rex 2562  df-v 2803  df-sbc 3005  df-un 3170  df-sn 3659  df-pr 3660  df-uni 3844  df-iota 5235
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