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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 12737 | . . 3 | |
2 | 1 | dmmptss 5094 | . 2 |
3 | df-br 3977 | . . 3 | |
4 | 1 | funmpt2 5221 | . . . . 5 |
5 | funrel 5199 | . . . . 5 | |
6 | 4, 5 | ax-mp 5 | . . . 4 |
7 | relelfvdm 5512 | . . . 4 | |
8 | 6, 7 | mpan 421 | . . 3 |
9 | 3, 8 | sylbi 120 | . 2 |
10 | 2, 9 | sseldi 3135 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 w3a 967 wcel 2135 wral 2442 wrex 2443 cop 3573 cuni 3783 class class class wbr 3976 copab 4036 cdm 4598 crn 4599 cres 4600 wrel 4603 wfun 5176 wf 5178 cfv 5182 (class class class)co 5836 cpm 6606 cc 7742 cuz 9457 ctop 12542 clm 12734 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-rab 2451 df-v 2723 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-br 3977 df-opab 4038 df-mpt 4039 df-id 4265 df-xp 4604 df-rel 4605 df-cnv 4606 df-co 4607 df-dm 4608 df-rn 4609 df-res 4610 df-ima 4611 df-iota 5147 df-fun 5184 df-fv 5190 df-lm 12737 |
This theorem is referenced by: lmcvg 12764 lmtopcnp 12797 |
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