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 5369 | . . . 4 | |
3 | funcnvcnv 5182 | . . . 4 | |
4 | 1, 2, 3 | 3syl 17 | . . 3 |
5 | f1ocnv 5380 | . . . . . . 7 | |
6 | 1, 5 | syl 14 | . . . . . 6 |
7 | f1of1 5366 | . . . . . 6 | |
8 | 6, 7 | syl 14 | . . . . 5 |
9 | ssrab2 3182 | . . . . 5 | |
10 | f1ores 5382 | . . . . 5 | |
11 | 8, 9, 10 | sylancl 409 | . . . 4 |
12 | f1oresrab.1 | . . . . . . 7 | |
13 | 12 | mptpreima 5032 | . . . . . 6 |
14 | f1oresrab.3 | . . . . . . . . . 10 | |
15 | 14 | 3expia 1183 | . . . . . . . . 9 |
16 | 15 | alrimiv 1846 | . . . . . . . 8 |
17 | f1of 5367 | . . . . . . . . . . 11 | |
18 | 1, 17 | syl 14 | . . . . . . . . . 10 |
19 | 12 | fmpt 5570 | . . . . . . . . . 10 |
20 | 18, 19 | sylibr 133 | . . . . . . . . 9 |
21 | 20 | r19.21bi 2520 | . . . . . . . 8 |
22 | elrab3t 2839 | . . . . . . . 8 | |
23 | 16, 21, 22 | syl2anc 408 | . . . . . . 7 |
24 | 23 | rabbidva 2674 | . . . . . 6 |
25 | 13, 24 | syl5eq 2184 | . . . . 5 |
26 | f1oeq3 5358 | . . . . 5 | |
27 | 25, 26 | syl 14 | . . . 4 |
28 | 11, 27 | mpbid 146 | . . 3 |
29 | f1orescnv 5383 | . . 3 | |
30 | 4, 28, 29 | syl2anc 408 | . 2 |
31 | rescnvcnv 5001 | . . 3 | |
32 | f1oeq1 5356 | . . 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 962 wal 1329 wceq 1331 wcel 1480 wral 2416 crab 2420 wss 3071 cmpt 3989 ccnv 4538 cres 4541 cima 4542 wfun 5117 wf 5119 wf1 5120 wf1o 5122 |
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-rab 2425 df-v 2688 df-sbc 2910 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-opab 3990 df-mpt 3991 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-iota 5088 df-fun 5125 df-fn 5126 df-f 5127 df-f1 5128 df-fo 5129 df-f1o 5130 df-fv 5131 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |