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Mirrors > Home > ILE Home > Th. List > idref | Unicode version |
Description: TODO: This is the same
as issref 4707 (which has a much longer proof).
Should we replace issref 4707 with this one? - NM 9-May-2016.
Two ways to state a relation is reflexive. (Adapted from Tarski.) (Contributed by FL, 15-Jan-2012.) (Proof shortened by Mario Carneiro, 3-Nov-2015.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
idref |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2040 | . . . 4 | |
2 | 1 | fmpt 5319 | . . 3 |
3 | vex 2560 | . . . . . 6 | |
4 | 3, 3 | opex 3966 | . . . . 5 |
5 | 4, 1 | fnmpti 5027 | . . . 4 |
6 | df-f 4906 | . . . 4 | |
7 | 5, 6 | mpbiran 847 | . . 3 |
8 | 2, 7 | bitri 173 | . 2 |
9 | df-br 3765 | . . 3 | |
10 | 9 | ralbii 2330 | . 2 |
11 | mptresid 4660 | . . . 4 | |
12 | 3 | fnasrn 5341 | . . . 4 |
13 | 11, 12 | eqtr3i 2062 | . . 3 |
14 | 13 | sseq1i 2969 | . 2 |
15 | 8, 10, 14 | 3bitr4ri 202 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 98 wcel 1393 wral 2306 wss 2917 cop 3378 class class class wbr 3764 cmpt 3818 cid 4025 crn 4346 cres 4347 wfn 4897 wf 4898 |
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-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-reu 2313 df-rab 2315 df-v 2559 df-sbc 2765 df-csb 2853 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-iun 3659 df-br 3765 df-opab 3819 df-mpt 3820 df-id 4030 df-xp 4351 df-rel 4352 df-cnv 4353 df-co 4354 df-dm 4355 df-rn 4356 df-res 4357 df-ima 4358 df-iota 4867 df-fun 4904 df-fn 4905 df-f 4906 df-f1 4907 df-fo 4908 df-f1o 4909 df-fv 4910 |
This theorem is referenced by: (None) |
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