Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > rescnvcnv | Unicode version |
Description: The restriction of the double converse of a class. (Contributed by NM, 8-Apr-2007.) (Proof shortened by Andrew Salmon, 27-Aug-2011.) |
Ref | Expression |
---|---|
rescnvcnv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnvcnv2 4962 | . . 3 | |
2 | 1 | reseq1i 4785 | . 2 |
3 | resres 4801 | . 2 | |
4 | ssv 3089 | . . . 4 | |
5 | sseqin2 3265 | . . . 4 | |
6 | 4, 5 | mpbi 144 | . . 3 |
7 | 6 | reseq2i 4786 | . 2 |
8 | 2, 3, 7 | 3eqtri 2142 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1316 cvv 2660 cin 3040 wss 3041 ccnv 4508 cres 4511 |
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-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-br 3900 df-opab 3960 df-xp 4515 df-rel 4516 df-cnv 4517 df-res 4521 |
This theorem is referenced by: cnvcnvres 4972 imacnvcnv 4973 resdm2 4999 resdmres 5000 coires1 5026 cocnvres 5033 f1oresrab 5553 |
Copyright terms: Public domain | W3C validator |