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Mirrors > Home > ILE Home > Th. List > fncnv | Unicode version |
Description: Single-rootedness (see funcnv 5259) 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 5201 | . 2 | |
2 | df-rn 4622 | . . . 4 | |
3 | 2 | eqeq1i 2178 | . . 3 |
4 | 3 | anbi2i 454 | . 2 |
5 | rninxp 5054 | . . . . 5 | |
6 | 5 | anbi1i 455 | . . . 4 |
7 | funcnv 5259 | . . . . . 6 | |
8 | raleq 2665 | . . . . . . 7 | |
9 | moanimv 2094 | . . . . . . . . . 10 | |
10 | brinxp2 4678 | . . . . . . . . . . . 12 | |
11 | 3anan12 985 | . . . . . . . . . . . 12 | |
12 | 10, 11 | bitri 183 | . . . . . . . . . . 11 |
13 | 12 | mobii 2056 | . . . . . . . . . 10 |
14 | df-rmo 2456 | . . . . . . . . . . 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 2484 | . . . . . . 7 |
20 | 8, 19 | bitrdi 195 | . . . . . 6 |
21 | 7, 20 | syl5bb 191 | . . . . 5 |
22 | 21 | pm5.32i 451 | . . . 4 |
23 | r19.26 2596 | . . . 4 | |
24 | 6, 22, 23 | 3bitr4i 211 | . . 3 |
25 | ancom 264 | . . 3 | |
26 | reu5 2682 | . . . 4 | |
27 | 26 | ralbii 2476 | . . 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 973 wceq 1348 wmo 2020 wcel 2141 wral 2448 wrex 2449 wreu 2450 wrmo 2451 cin 3120 class class class wbr 3989 cxp 4609 ccnv 4610 cdm 4611 crn 4612 wfun 5192 wfn 5193 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-reu 2455 df-rmo 2456 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-br 3990 df-opab 4051 df-id 4278 df-xp 4617 df-rel 4618 df-cnv 4619 df-co 4620 df-dm 4621 df-rn 4622 df-res 4623 df-ima 4624 df-fun 5200 df-fn 5201 |
This theorem is referenced by: (None) |
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