Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > f1oresrab | Unicode version |
Description: Build a bijection between restricted abstract builders, given a bijection between the base classes, deduction version. (Contributed by Thierry Arnoux, 17-Aug-2018.) |
Ref | Expression |
---|---|
f1oresrab.1 | |
f1oresrab.2 | |
f1oresrab.3 |
Ref | Expression |
---|---|
f1oresrab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1oresrab.2 | . . . 4 | |
2 | f1ofun 5337 | . . . 4 | |
3 | funcnvcnv 5152 | . . . 4 | |
4 | 1, 2, 3 | 3syl 17 | . . 3 |
5 | f1ocnv 5348 | . . . . . . 7 | |
6 | 1, 5 | syl 14 | . . . . . 6 |
7 | f1of1 5334 | . . . . . 6 | |
8 | 6, 7 | syl 14 | . . . . 5 |
9 | ssrab2 3152 | . . . . 5 | |
10 | f1ores 5350 | . . . . 5 | |
11 | 8, 9, 10 | sylancl 409 | . . . 4 |
12 | f1oresrab.1 | . . . . . . 7 | |
13 | 12 | mptpreima 5002 | . . . . . 6 |
14 | f1oresrab.3 | . . . . . . . . . 10 | |
15 | 14 | 3expia 1168 | . . . . . . . . 9 |
16 | 15 | alrimiv 1830 | . . . . . . . 8 |
17 | f1of 5335 | . . . . . . . . . . 11 | |
18 | 1, 17 | syl 14 | . . . . . . . . . 10 |
19 | 12 | fmpt 5538 | . . . . . . . . . 10 |
20 | 18, 19 | sylibr 133 | . . . . . . . . 9 |
21 | 20 | r19.21bi 2497 | . . . . . . . 8 |
22 | elrab3t 2812 | . . . . . . . 8 | |
23 | 16, 21, 22 | syl2anc 408 | . . . . . . 7 |
24 | 23 | rabbidva 2648 | . . . . . 6 |
25 | 13, 24 | syl5eq 2162 | . . . . 5 |
26 | f1oeq3 5328 | . . . . 5 | |
27 | 25, 26 | syl 14 | . . . 4 |
28 | 11, 27 | mpbid 146 | . . 3 |
29 | f1orescnv 5351 | . . 3 | |
30 | 4, 28, 29 | syl2anc 408 | . 2 |
31 | rescnvcnv 4971 | . . 3 | |
32 | f1oeq1 5326 | . . 3 | |
33 | 31, 32 | ax-mp 5 | . 2 |
34 | 30, 33 | sylib 121 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 947 wal 1314 wceq 1316 wcel 1465 wral 2393 crab 2397 wss 3041 cmpt 3959 ccnv 4508 cres 4511 cima 4512 wfun 5087 wf 5089 wf1 5090 wf1o 5092 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-rab 2402 df-v 2662 df-sbc 2883 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-mpt 3961 df-id 4185 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-rn 4520 df-res 4521 df-ima 4522 df-iota 5058 df-fun 5095 df-fn 5096 df-f 5097 df-f1 5098 df-fo 5099 df-f1o 5100 df-fv 5101 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |