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Mirrors > Home > ILE Home > Th. List > spcimedv | Unicode version |
Description: Restricted existential specialization, using implicit substitution. (Contributed by Mario Carneiro, 4-Jan-2017.) |
Ref | Expression |
---|---|
spcimdv.1 | |
spcimedv.2 |
Ref | Expression |
---|---|
spcimedv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | spcimedv.2 | . . . 4 | |
2 | 1 | ex 114 | . . 3 |
3 | 2 | alrimiv 1867 | . 2 |
4 | spcimdv.1 | . 2 | |
5 | nfv 1521 | . . 3 | |
6 | nfcv 2312 | . . 3 | |
7 | 5, 6 | spcimegft 2808 | . 2 |
8 | 3, 4, 7 | sylc 62 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1346 wceq 1348 wex 1485 wcel 2141 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 |
This theorem is referenced by: rspcimedv 2836 fihashf1rn 10710 |
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