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Mirrors > Home > ILE Home > Th. List > fncnv | Unicode version |
Description: Single-rootedness (see funcnv 5231) 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 5173 | . 2 | |
2 | df-rn 4597 | . . . 4 | |
3 | 2 | eqeq1i 2165 | . . 3 |
4 | 3 | anbi2i 453 | . 2 |
5 | rninxp 5029 | . . . . 5 | |
6 | 5 | anbi1i 454 | . . . 4 |
7 | funcnv 5231 | . . . . . 6 | |
8 | raleq 2652 | . . . . . . 7 | |
9 | moanimv 2081 | . . . . . . . . . 10 | |
10 | brinxp2 4653 | . . . . . . . . . . . 12 | |
11 | 3anan12 975 | . . . . . . . . . . . 12 | |
12 | 10, 11 | bitri 183 | . . . . . . . . . . 11 |
13 | 12 | mobii 2043 | . . . . . . . . . 10 |
14 | df-rmo 2443 | . . . . . . . . . . 11 | |
15 | 14 | imbi2i 225 | . . . . . . . . . 10 |
16 | 9, 13, 15 | 3bitr4i 211 | . . . . . . . . 9 |
17 | biimt 240 | . . . . . . . . 9 | |
18 | 16, 17 | bitr4id 198 | . . . . . . . 8 |
19 | 18 | ralbiia 2471 | . . . . . . 7 |
20 | 8, 19 | bitrdi 195 | . . . . . 6 |
21 | 7, 20 | syl5bb 191 | . . . . 5 |
22 | 21 | pm5.32i 450 | . . . 4 |
23 | r19.26 2583 | . . . 4 | |
24 | 6, 22, 23 | 3bitr4i 211 | . . 3 |
25 | ancom 264 | . . 3 | |
26 | reu5 2669 | . . . 4 | |
27 | 26 | ralbii 2463 | . . 3 |
28 | 24, 25, 27 | 3bitr4i 211 | . 2 |
29 | 1, 4, 28 | 3bitr2i 207 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 963 wceq 1335 wmo 2007 wcel 2128 wral 2435 wrex 2436 wreu 2437 wrmo 2438 cin 3101 class class class wbr 3965 cxp 4584 ccnv 4585 cdm 4586 crn 4587 wfun 5164 wfn 5165 |
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-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-14 2131 ax-ext 2139 ax-sep 4082 ax-pow 4135 ax-pr 4169 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 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-reu 2442 df-rmo 2443 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-br 3966 df-opab 4026 df-id 4253 df-xp 4592 df-rel 4593 df-cnv 4594 df-co 4595 df-dm 4596 df-rn 4597 df-res 4598 df-ima 4599 df-fun 5172 df-fn 5173 |
This theorem is referenced by: (None) |
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