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Mirrors > Home > ILE Home > Th. List > fncnv | Unicode version |
Description: Single-rootedness (see funcnv 4960) of a class cut down by a cross product. (Contributed by NM, 5-Mar-2007.) |
Ref | Expression |
---|---|
fncnv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-fn 4905 | . 2 | |
2 | df-rn 4356 | . . . 4 | |
3 | 2 | eqeq1i 2047 | . . 3 |
4 | 3 | anbi2i 430 | . 2 |
5 | rninxp 4764 | . . . . 5 | |
6 | 5 | anbi1i 431 | . . . 4 |
7 | funcnv 4960 | . . . . . 6 | |
8 | raleq 2505 | . . . . . . 7 | |
9 | biimt 230 | . . . . . . . . 9 | |
10 | moanimv 1975 | . . . . . . . . . 10 | |
11 | brinxp2 4407 | . . . . . . . . . . . 12 | |
12 | 3anan12 897 | . . . . . . . . . . . 12 | |
13 | 11, 12 | bitri 173 | . . . . . . . . . . 11 |
14 | 13 | mobii 1937 | . . . . . . . . . 10 |
15 | df-rmo 2314 | . . . . . . . . . . 11 | |
16 | 15 | imbi2i 215 | . . . . . . . . . 10 |
17 | 10, 14, 16 | 3bitr4i 201 | . . . . . . . . 9 |
18 | 9, 17 | syl6rbbr 188 | . . . . . . . 8 |
19 | 18 | ralbiia 2338 | . . . . . . 7 |
20 | 8, 19 | syl6bb 185 | . . . . . 6 |
21 | 7, 20 | syl5bb 181 | . . . . 5 |
22 | 21 | pm5.32i 427 | . . . 4 |
23 | r19.26 2441 | . . . 4 | |
24 | 6, 22, 23 | 3bitr4i 201 | . . 3 |
25 | ancom 253 | . . 3 | |
26 | reu5 2522 | . . . 4 | |
27 | 26 | ralbii 2330 | . . 3 |
28 | 24, 25, 27 | 3bitr4i 201 | . 2 |
29 | 1, 4, 28 | 3bitr2i 197 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 w3a 885 wceq 1243 wcel 1393 wmo 1901 wral 2306 wrex 2307 wreu 2308 wrmo 2309 cin 2916 class class class wbr 3764 cxp 4343 ccnv 4344 cdm 4345 crn 4346 wfun 4896 wfn 4897 |
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-rmo 2314 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-br 3765 df-opab 3819 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-fun 4904 df-fn 4905 |
This theorem is referenced by: (None) |
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