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Theorem iprc 4527
Description: The identity function is a proper class. This means, for example, that we cannot use it as a member of the class of continuous functions unless it is restricted to a set. (Contributed by NM, 1-Jan-2007.)
Assertion
Ref Expression
iprc ¬ I V

Proof of Theorem iprc
StepHypRef Expression
1 vprc 3862 . . 3 ¬ V V
2 dmi 4477 . . . 4 dom I = V
32eleq1i 2085 . . 3 (dom I V ↔ V V)
41, 3mtbir 583 . 2 ¬ dom I V
5 dmexg 4523 . 2 ( I V → dom I V)
64, 5mto 575 1 ¬ I V
Colors of variables: wff set class
Syntax hints:  ¬ wn 3   wcel 1374  Vcvv 2535   I cid 3999  dom cdm 4272
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 532  ax-in2 533  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-13 1385  ax-14 1386  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004  ax-sep 3849  ax-pow 3901  ax-pr 3918  ax-un 4120
This theorem depends on definitions:  df-bi 110  df-3an 875  df-tru 1231  df-fal 1234  df-nf 1330  df-sb 1628  df-eu 1885  df-mo 1886  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-ral 2289  df-rex 2290  df-v 2537  df-un 2899  df-in 2901  df-ss 2908  df-pw 3336  df-sn 3356  df-pr 3357  df-op 3359  df-uni 3555  df-br 3739  df-opab 3793  df-id 4004  df-xp 4278  df-rel 4279  df-cnv 4280  df-dm 4282  df-rn 4283
This theorem is referenced by: (None)
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