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Theorem iprc 7613
 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, as in idcn 21903. (Contributed by NM, 1-Jan-2007.)
Assertion
Ref Expression
iprc ¬ I ∈ V

Proof of Theorem iprc
StepHypRef Expression
1 dmi 5761 . . 3 dom I = V
2 vprc 5187 . . 3 ¬ V ∈ V
31, 2eqneltri 2883 . 2 ¬ dom I ∈ V
4 dmexg 7607 . 2 ( I ∈ V → dom I ∈ V)
53, 4mto 200 1 ¬ I ∈ V
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   ∈ wcel 2111  Vcvv 3442   I cid 5428  dom cdm 5523 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-10 2142  ax-11 2158  ax-12 2175  ax-ext 2770  ax-sep 5171  ax-nul 5178  ax-pr 5299  ax-un 7454 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-mo 2598  df-eu 2629  df-clab 2777  df-cleq 2791  df-clel 2870  df-nfc 2938  df-ral 3111  df-rex 3112  df-rab 3115  df-v 3444  df-dif 3886  df-un 3888  df-in 3890  df-ss 3900  df-nul 4247  df-if 4429  df-sn 4529  df-pr 4531  df-op 4535  df-uni 4805  df-br 5035  df-opab 5097  df-id 5429  df-xp 5529  df-rel 5530  df-cnv 5531  df-dm 5533  df-rn 5534 This theorem is referenced by: (None)
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