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Mirrors > Home > ILE Home > Th. List > rspc | Unicode version |
Description: Restricted specialization, using implicit substitution. (Contributed by NM, 19-Apr-2005.) (Revised by Mario Carneiro, 11-Oct-2016.) |
Ref | Expression |
---|---|
rspc.1 | |
rspc.2 |
Ref | Expression |
---|---|
rspc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2398 | . 2 | |
2 | nfcv 2258 | . . . 4 | |
3 | nfv 1493 | . . . . 5 | |
4 | rspc.1 | . . . . 5 | |
5 | 3, 4 | nfim 1536 | . . . 4 |
6 | eleq1 2180 | . . . . 5 | |
7 | rspc.2 | . . . . 5 | |
8 | 6, 7 | imbi12d 233 | . . . 4 |
9 | 2, 5, 8 | spcgf 2742 | . . 3 |
10 | 9 | pm2.43a 51 | . 2 |
11 | 1, 10 | syl5bi 151 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1314 wceq 1316 wnf 1421 wcel 1465 wral 2393 |
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-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-v 2662 |
This theorem is referenced by: rspcv 2759 rspc2 2774 pofun 4204 omsinds 4505 fmptcof 5555 fliftfuns 5667 qliftfuns 6481 xpf1o 6706 finexdc 6764 ssfirab 6790 iunfidisj 6802 lble 8669 exfzdc 9972 uzsinds 10170 sumeq2 11083 sumfct 11098 sumrbdclem 11100 summodclem3 11104 summodclem2a 11105 zsumdc 11108 fsumgcl 11110 fsum3 11111 fsumf1o 11114 isumss 11115 isumss2 11117 fsum3cvg2 11118 fsumadd 11130 isummulc2 11150 fsum2dlemstep 11158 fisumcom2 11162 fsumshftm 11169 fisum0diag2 11171 fsummulc2 11172 fsum00 11186 fsumabs 11189 fsumrelem 11195 fsumiun 11201 isumshft 11214 mertenslem2 11260 zsupcllemstep 11550 infssuzex 11554 bezoutlemmain 11598 ctiunctlemudc 11861 iuncld 12195 txcnp 12351 fsumcncntop 12636 bj-nntrans 13045 |
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