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Mirrors > Home > ILE Home > Th. List > fncnv | Unicode version |
Description: Single-rootedness (see funcnv 5184) 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 5126 | . 2 | |
2 | df-rn 4550 | . . . 4 | |
3 | 2 | eqeq1i 2147 | . . 3 |
4 | 3 | anbi2i 452 | . 2 |
5 | rninxp 4982 | . . . . 5 | |
6 | 5 | anbi1i 453 | . . . 4 |
7 | funcnv 5184 | . . . . . 6 | |
8 | raleq 2626 | . . . . . . 7 | |
9 | biimt 240 | . . . . . . . . 9 | |
10 | moanimv 2074 | . . . . . . . . . 10 | |
11 | brinxp2 4606 | . . . . . . . . . . . 12 | |
12 | 3anan12 974 | . . . . . . . . . . . 12 | |
13 | 11, 12 | bitri 183 | . . . . . . . . . . 11 |
14 | 13 | mobii 2036 | . . . . . . . . . 10 |
15 | df-rmo 2424 | . . . . . . . . . . 11 | |
16 | 15 | imbi2i 225 | . . . . . . . . . 10 |
17 | 10, 14, 16 | 3bitr4i 211 | . . . . . . . . 9 |
18 | 9, 17 | syl6rbbr 198 | . . . . . . . 8 |
19 | 18 | ralbiia 2449 | . . . . . . 7 |
20 | 8, 19 | syl6bb 195 | . . . . . 6 |
21 | 7, 20 | syl5bb 191 | . . . . 5 |
22 | 21 | pm5.32i 449 | . . . 4 |
23 | r19.26 2558 | . . . 4 | |
24 | 6, 22, 23 | 3bitr4i 211 | . . 3 |
25 | ancom 264 | . . 3 | |
26 | reu5 2643 | . . . 4 | |
27 | 26 | ralbii 2441 | . . 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 962 wceq 1331 wcel 1480 wmo 2000 wral 2416 wrex 2417 wreu 2418 wrmo 2419 cin 3070 class class class wbr 3929 cxp 4537 ccnv 4538 cdm 4539 crn 4540 wfun 5117 wfn 5118 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-reu 2423 df-rmo 2424 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-br 3930 df-opab 3990 df-id 4215 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-rn 4550 df-res 4551 df-ima 4552 df-fun 5125 df-fn 5126 |
This theorem is referenced by: (None) |
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