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Mirrors > Home > ILE Home > Th. List > rspce | Unicode version |
Description: Restricted existential specialization, using implicit substitution. (Contributed by NM, 26-May-1998.) (Revised by Mario Carneiro, 11-Oct-2016.) |
Ref | Expression |
---|---|
rspc.1 | |
rspc.2 |
Ref | Expression |
---|---|
rspce |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2308 | . . . 4 | |
2 | nfv 1516 | . . . . 5 | |
3 | rspc.1 | . . . . 5 | |
4 | 2, 3 | nfan 1553 | . . . 4 |
5 | eleq1 2229 | . . . . 5 | |
6 | rspc.2 | . . . . 5 | |
7 | 5, 6 | anbi12d 465 | . . . 4 |
8 | 1, 4, 7 | spcegf 2809 | . . 3 |
9 | 8 | anabsi5 569 | . 2 |
10 | df-rex 2450 | . 2 | |
11 | 9, 10 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1343 wnf 1448 wex 1480 wcel 2136 wrex 2445 |
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 1435 ax-7 1436 ax-gen 1437 ax-ie1 1481 ax-ie2 1482 ax-8 1492 ax-10 1493 ax-11 1494 ax-i12 1495 ax-bndl 1497 ax-4 1498 ax-17 1514 ax-i9 1518 ax-ial 1522 ax-i5r 1523 ax-ext 2147 |
This theorem depends on definitions: df-bi 116 df-tru 1346 df-nf 1449 df-sb 1751 df-clab 2152 df-cleq 2158 df-clel 2161 df-nfc 2297 df-rex 2450 df-v 2728 |
This theorem is referenced by: rspcev 2830 bezoutlemmain 11931 |
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