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Mirrors > Home > ILE Home > Th. List > lmrcl | Unicode version |
Description: Reverse closure for the convergence relation. (Contributed by Mario Carneiro, 7-Sep-2015.) |
Ref | Expression |
---|---|
lmrcl |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-lm 12286 | . . 3 | |
2 | 1 | dmmptss 5005 | . 2 |
3 | df-br 3900 | . . 3 | |
4 | 1 | funmpt2 5132 | . . . . 5 |
5 | funrel 5110 | . . . . 5 | |
6 | 4, 5 | ax-mp 5 | . . . 4 |
7 | relelfvdm 5421 | . . . 4 | |
8 | 6, 7 | mpan 420 | . . 3 |
9 | 3, 8 | sylbi 120 | . 2 |
10 | 2, 9 | sseldi 3065 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 w3a 947 wcel 1465 wral 2393 wrex 2394 cop 3500 cuni 3706 class class class wbr 3899 copab 3958 cdm 4509 crn 4510 cres 4511 wrel 4514 wfun 5087 wf 5089 cfv 5093 (class class class)co 5742 cpm 6511 cc 7586 cuz 9294 ctop 12091 clm 12283 |
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-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-fv 5101 df-lm 12286 |
This theorem is referenced by: lmcvg 12313 lmtopcnp 12346 |
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