Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > fliftcnv | Unicode version |
Description: Converse of the relation . (Contributed by Mario Carneiro, 23-Dec-2016.) |
Ref | Expression |
---|---|
flift.1 | |
flift.2 | |
flift.3 |
Ref | Expression |
---|---|
fliftcnv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2117 | . . . . 5 | |
2 | flift.3 | . . . . 5 | |
3 | flift.2 | . . . . 5 | |
4 | 1, 2, 3 | fliftrel 5661 | . . . 4 |
5 | relxp 4618 | . . . 4 | |
6 | relss 4596 | . . . 4 | |
7 | 4, 5, 6 | mpisyl 1407 | . . 3 |
8 | relcnv 4887 | . . 3 | |
9 | 7, 8 | jctil 310 | . 2 |
10 | flift.1 | . . . . . . 7 | |
11 | 10, 3, 2 | fliftel 5662 | . . . . . 6 |
12 | vex 2663 | . . . . . . 7 | |
13 | vex 2663 | . . . . . . 7 | |
14 | 12, 13 | brcnv 4692 | . . . . . 6 |
15 | ancom 264 | . . . . . . 7 | |
16 | 15 | rexbii 2419 | . . . . . 6 |
17 | 11, 14, 16 | 3bitr4g 222 | . . . . 5 |
18 | 1, 2, 3 | fliftel 5662 | . . . . 5 |
19 | 17, 18 | bitr4d 190 | . . . 4 |
20 | df-br 3900 | . . . 4 | |
21 | df-br 3900 | . . . 4 | |
22 | 19, 20, 21 | 3bitr3g 221 | . . 3 |
23 | 22 | eqrelrdv2 4608 | . 2 |
24 | 9, 23 | mpancom 418 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1316 wcel 1465 wrex 2394 wss 3041 cop 3500 class class class wbr 3899 cmpt 3959 cxp 4507 ccnv 4508 crn 4510 wrel 4514 |
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-fv 5101 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |