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Mirrors > Home > ILE Home > Th. List > resubcld | Unicode version |
Description: Closure law for subtraction of reals. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
renegcld.1 | |
resubcld.2 |
Ref | Expression |
---|---|
resubcld |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | renegcld.1 | . 2 | |
2 | resubcld.2 | . 2 | |
3 | resubcl 7275 | . 2 | |
4 | 1, 2, 3 | syl2anc 391 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1393 (class class class)co 5512 cr 6888 cmin 7182 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 ax-setind 4262 ax-resscn 6976 ax-1cn 6977 ax-icn 6979 ax-addcl 6980 ax-addrcl 6981 ax-mulcl 6982 ax-addcom 6984 ax-addass 6986 ax-distr 6988 ax-i2m1 6989 ax-0id 6992 ax-rnegex 6993 ax-cnre 6995 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-fal 1249 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ne 2206 df-ral 2311 df-rex 2312 df-reu 2313 df-rab 2315 df-v 2559 df-sbc 2765 df-dif 2920 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-br 3765 df-opab 3819 df-id 4030 df-xp 4351 df-rel 4352 df-cnv 4353 df-co 4354 df-dm 4355 df-iota 4867 df-fun 4904 df-fv 4910 df-riota 5468 df-ov 5515 df-oprab 5516 df-mpt2 5517 df-sub 7184 df-neg 7185 |
This theorem is referenced by: ltsubadd 7427 lesubadd 7429 ltaddsub 7431 leaddsub 7433 lesub1 7451 lesub2 7452 ltsub1 7453 ltsub2 7454 lt2sub 7455 le2sub 7456 rereim 7577 ltmul1a 7582 cru 7593 lemul1a 7824 ztri3or 8288 lincmb01cmp 8871 iccf1o 8872 rebtwn2z 9109 qbtwnrelemcalc 9110 qbtwnre 9111 intfracq 9162 modqval 9166 modqlt 9175 serile 9253 expnbnd 9372 crre 9457 remullem 9471 recvguniqlem 9592 resqrexlemover 9608 resqrexlemcalc2 9613 resqrexlemcalc3 9614 resqrexlemnmsq 9615 resqrexlemnm 9616 resqrexlemcvg 9617 resqrexlemglsq 9620 resqrexlemga 9621 fzomaxdiflem 9708 caubnd2 9713 amgm2 9714 icodiamlt 9776 qdenre 9798 mulcn2 9833 climle 9854 climsqz 9855 climsqz2 9856 climcvg1nlem 9868 |
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