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Mirrors > Home > MPE Home > Th. List > iprc | Unicode version |
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.) |
Ref | Expression |
---|---|
iprc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vprc 4590 | . . 3 | |
2 | dmi 5222 | . . . 4 | |
3 | 2 | eleq1i 2534 | . . 3 |
4 | 1, 3 | mtbir 299 | . 2 |
5 | dmexg 6731 | . 2 | |
6 | 4, 5 | mto 176 | 1 |
Colors of variables: wff setvar class |
Syntax hints: -. wn 3 e. wcel 1818
cvv 3109
cid 4795
dom cdm 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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