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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 2488 |
. 2
| |
| 2 | nfcv 2347 |
. . . 4
| |
| 3 | nfv 1550 |
. . . . 5
| |
| 4 | rspc.1 |
. . . . 5
| |
| 5 | 3, 4 | nfim 1594 |
. . . 4
|
| 6 | eleq1 2267 |
. . . . 5
| |
| 7 | rspc.2 |
. . . . 5
| |
| 8 | 6, 7 | imbi12d 234 |
. . . 4
|
| 9 | 2, 5, 8 | spcgf 2854 |
. . 3
|
| 10 | 9 | pm2.43a 51 |
. 2
|
| 11 | 1, 10 | biimtrid 152 |
1
|
| Colors of variables: wff set class |
| Syntax hints: |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1469 ax-7 1470 ax-gen 1471 ax-ie1 1515 ax-ie2 1516 ax-8 1526 ax-10 1527 ax-11 1528 ax-i12 1529 ax-bndl 1531 ax-4 1532 ax-17 1548 ax-i9 1552 ax-ial 1556 ax-i5r 1557 ax-ext 2186 |
| This theorem depends on definitions: df-bi 117 df-tru 1375 df-nf 1483 df-sb 1785 df-clab 2191 df-cleq 2197 df-clel 2200 df-nfc 2336 df-ral 2488 df-v 2773 |
| This theorem is referenced by: rspcv 2872 rspc2 2887 rspc2vd 3161 pofun 4358 omsinds 4669 fmptcof 5746 fliftfuns 5866 qliftfuns 6705 xpf1o 6940 finexdc 6998 ssfirab 7032 opabfi 7034 iunfidisj 7047 dcfi 7082 cc3 7379 lble 9019 exfzdc 10367 zsupcllemstep 10370 infssuzex 10374 uzsinds 10587 sumeq2 11641 sumfct 11656 sumrbdclem 11659 summodclem3 11662 summodclem2a 11663 zsumdc 11666 fsumgcl 11668 fsum3 11669 fsumf1o 11672 isumss 11673 isumss2 11675 fsum3cvg2 11676 fsumadd 11688 isummulc2 11708 fsum2dlemstep 11716 fisumcom2 11720 fsumshftm 11727 fisum0diag2 11729 fsummulc2 11730 fsum00 11744 fsumabs 11747 fsumrelem 11753 fsumiun 11759 isumshft 11772 mertenslem2 11818 prodeq2 11839 prodrbdclem 11853 prodmodclem3 11857 prodmodclem2a 11858 zproddc 11861 fprodseq 11865 prodfct 11869 fprodf1o 11870 prodssdc 11871 fprodmul 11873 fprodm1s 11883 fprodp1s 11884 fprodabs 11898 fprodap0 11903 fprod2dlemstep 11904 fprodcom2fi 11908 fprodrec 11911 fprodap0f 11918 fprodle 11922 bezoutlemmain 12290 nnwosdc 12331 pcmpt 12637 ctiunctlemudc 12779 gsumfzfsumlemm 14320 iuncld 14558 txcnp 14714 fsumcncntop 15010 bj-nntrans 15849 |
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