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Mirrors > Home > ILE 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. (Contributed by NM, 1-Jan-2007.) |
Ref | Expression |
---|---|
iprc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vprc 4098 | . . 3 | |
2 | dmi 4803 | . . . 4 | |
3 | 2 | eleq1i 2223 | . . 3 |
4 | 1, 3 | mtbir 661 | . 2 |
5 | dmexg 4852 | . 2 | |
6 | 4, 5 | mto 652 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wcel 2128 cvv 2712 cid 4250 cdm 4588 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-13 2130 ax-14 2131 ax-ext 2139 ax-sep 4084 ax-pow 4137 ax-pr 4171 ax-un 4395 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-fal 1341 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3546 df-sn 3567 df-pr 3568 df-op 3570 df-uni 3775 df-br 3968 df-opab 4028 df-id 4255 df-xp 4594 df-rel 4595 df-cnv 4596 df-dm 4598 df-rn 4599 |
This theorem is referenced by: (None) |
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