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Mirrors > Home > ILE Home > Th. List > rspcedvd | Unicode version |
Description: Restricted existential specialization, using implicit substitution. Variant of rspcedv 2705. (Contributed by AV, 27-Nov-2019.) |
Ref | Expression |
---|---|
rspcedvd.1 | |
rspcedvd.2 | |
rspcedvd.3 |
Ref | Expression |
---|---|
rspcedvd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rspcedvd.3 | . 2 | |
2 | rspcedvd.1 | . . 3 | |
3 | rspcedvd.2 | . . 3 | |
4 | 2, 3 | rspcedv 2705 | . 2 |
5 | 1, 4 | mpd 13 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wceq 1284 wcel 1433 wrex 2349 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-rex 2354 df-v 2603 |
This theorem is referenced by: rspcedeq1vd 2709 rspcedeq2vd 2710 modqmuladd 9368 modqmuladdnn0 9370 modfzo0difsn 9397 negfi 10110 divconjdvds 10249 2tp1odd 10284 dfgcd2 10403 qredeu 10479 pw2dvdslemn 10543 |
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