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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 941 | . 2 | |
2 | simpl2 942 | . 2 | |
3 | rspc3v.3 | . . . 4 | |
4 | 3 | rspcev 2701 | . . 3 |
5 | 4 | 3ad2antl3 1102 | . 2 |
6 | rspc3v.1 | . . . 4 | |
7 | 6 | rexbidv 2369 | . . 3 |
8 | rspc3v.2 | . . . 4 | |
9 | 8 | rexbidv 2369 | . . 3 |
10 | 7, 9 | rspc2ev 2715 | . 2 |
11 | 1, 2, 5, 10 | syl3anc 1169 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 w3a 919 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-3an 921 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: (None) |
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