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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 2137 | . . . . 5 | |
2 | flift.3 | . . . . 5 | |
3 | flift.2 | . . . . 5 | |
4 | 1, 2, 3 | fliftrel 5686 | . . . 4 |
5 | relxp 4643 | . . . 4 | |
6 | relss 4621 | . . . 4 | |
7 | 4, 5, 6 | mpisyl 1422 | . . 3 |
8 | relcnv 4912 | . . 3 | |
9 | 7, 8 | jctil 310 | . 2 |
10 | flift.1 | . . . . . . 7 | |
11 | 10, 3, 2 | fliftel 5687 | . . . . . 6 |
12 | vex 2684 | . . . . . . 7 | |
13 | vex 2684 | . . . . . . 7 | |
14 | 12, 13 | brcnv 4717 | . . . . . 6 |
15 | ancom 264 | . . . . . . 7 | |
16 | 15 | rexbii 2440 | . . . . . 6 |
17 | 11, 14, 16 | 3bitr4g 222 | . . . . 5 |
18 | 1, 2, 3 | fliftel 5687 | . . . . 5 |
19 | 17, 18 | bitr4d 190 | . . . 4 |
20 | df-br 3925 | . . . 4 | |
21 | df-br 3925 | . . . 4 | |
22 | 19, 20, 21 | 3bitr3g 221 | . . 3 |
23 | 22 | eqrelrdv2 4633 | . 2 |
24 | 9, 23 | mpancom 418 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1331 wcel 1480 wrex 2415 wss 3066 cop 3525 class class class wbr 3924 cmpt 3984 cxp 4532 ccnv 4533 crn 4535 wrel 4539 |
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 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-rab 2423 df-v 2683 df-sbc 2905 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-opab 3985 df-mpt 3986 df-id 4210 df-xp 4540 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-rn 4545 df-res 4546 df-ima 4547 df-iota 5083 df-fun 5120 df-fn 5121 df-f 5122 df-fv 5126 |
This theorem is referenced by: (None) |
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