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Theorem iprc 6735
 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 19758. (Contributed by NM, 1-Jan-2007.)
Assertion
Ref Expression
iprc

Proof of Theorem iprc
StepHypRef Expression
1 vprc 4590 . . 3
2 dmi 5222 . . . 4
32eleq1i 2534 . . 3
41, 3mtbir 299 . 2
5 dmexg 6731 . 2
64, 5mto 176 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  e.wcel 1818   cvv 3109   cid 4795  domcdm 5004 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-8 1820  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691  ax-un 6592 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-opab 4511  df-id 4800  df-xp 5010  df-rel 5011  df-cnv 5012  df-dm 5014  df-rn 5015
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