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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 2279 | . . . 4 | |
2 | nfv 1508 | . . . . 5 | |
3 | rspc.1 | . . . . 5 | |
4 | 2, 3 | nfan 1544 | . . . 4 |
5 | eleq1 2200 | . . . . 5 | |
6 | rspc.2 | . . . . 5 | |
7 | 5, 6 | anbi12d 464 | . . . 4 |
8 | 1, 4, 7 | spcegf 2764 | . . 3 |
9 | 8 | anabsi5 568 | . 2 |
10 | df-rex 2420 | . 2 | |
11 | 9, 10 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wnf 1436 wex 1468 wcel 1480 wrex 2415 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-rex 2420 df-v 2683 |
This theorem is referenced by: rspcev 2784 bezoutlemmain 11675 |
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