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Mirrors > Home > ILE Home > Th. List > rspc3ev | Unicode version |
Description: 3-variable restricted existentional specialization, using implicit substitution. (Contributed by NM, 25-Jul-2012.) |
Ref | Expression |
---|---|
rspc3v.1 | |
rspc3v.2 | |
rspc3v.3 |
Ref | Expression |
---|---|
rspc3ev |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl1 907 | . 2 | |
2 | simpl2 908 | . 2 | |
3 | rspc3v.3 | . . . 4 | |
4 | 3 | rspcev 2656 | . . 3 |
5 | 4 | 3ad2antl3 1068 | . 2 |
6 | rspc3v.1 | . . . 4 | |
7 | 6 | rexbidv 2327 | . . 3 |
8 | rspc3v.2 | . . . 4 | |
9 | 8 | rexbidv 2327 | . . 3 |
10 | 7, 9 | rspc2ev 2664 | . 2 |
11 | 1, 2, 5, 10 | syl3anc 1135 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 w3a 885 wceq 1243 wcel 1393 wrex 2307 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-v 2559 |
This theorem is referenced by: (None) |
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