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Mirrors > Home > ILE Home > Th. List > fncnv | Unicode version |
Description: Single-rootedness (see funcnv 4980) 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 4925 | . 2 | |
2 | df-rn 4374 | . . . 4 | |
3 | 2 | eqeq1i 2088 | . . 3 |
4 | 3 | anbi2i 444 | . 2 |
5 | rninxp 4784 | . . . . 5 | |
6 | 5 | anbi1i 445 | . . . 4 |
7 | funcnv 4980 | . . . . . 6 | |
8 | raleq 2549 | . . . . . . 7 | |
9 | biimt 239 | . . . . . . . . 9 | |
10 | moanimv 2016 | . . . . . . . . . 10 | |
11 | brinxp2 4425 | . . . . . . . . . . . 12 | |
12 | 3anan12 931 | . . . . . . . . . . . 12 | |
13 | 11, 12 | bitri 182 | . . . . . . . . . . 11 |
14 | 13 | mobii 1978 | . . . . . . . . . 10 |
15 | df-rmo 2356 | . . . . . . . . . . 11 | |
16 | 15 | imbi2i 224 | . . . . . . . . . 10 |
17 | 10, 14, 16 | 3bitr4i 210 | . . . . . . . . 9 |
18 | 9, 17 | syl6rbbr 197 | . . . . . . . 8 |
19 | 18 | ralbiia 2380 | . . . . . . 7 |
20 | 8, 19 | syl6bb 194 | . . . . . 6 |
21 | 7, 20 | syl5bb 190 | . . . . 5 |
22 | 21 | pm5.32i 441 | . . . 4 |
23 | r19.26 2485 | . . . 4 | |
24 | 6, 22, 23 | 3bitr4i 210 | . . 3 |
25 | ancom 262 | . . 3 | |
26 | reu5 2566 | . . . 4 | |
27 | 26 | ralbii 2372 | . . 3 |
28 | 24, 25, 27 | 3bitr4i 210 | . 2 |
29 | 1, 4, 28 | 3bitr2i 206 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 w3a 919 wceq 1284 wcel 1433 wmo 1942 wral 2348 wrex 2349 wreu 2350 wrmo 2351 cin 2972 class class class wbr 3785 cxp 4361 ccnv 4362 cdm 4363 crn 4364 wfun 4916 wfn 4917 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-reu 2355 df-rmo 2356 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-br 3786 df-opab 3840 df-id 4048 df-xp 4369 df-rel 4370 df-cnv 4371 df-co 4372 df-dm 4373 df-rn 4374 df-res 4375 df-ima 4376 df-fun 4924 df-fn 4925 |
This theorem is referenced by: (None) |
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