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Mirrors > Home > ILE Home > Th. List > rspct | Unicode version |
Description: A closed version of rspc 2650. (Contributed by Andrew Salmon, 6-Jun-2011.) |
Ref | Expression |
---|---|
rspct.1 |
Ref | Expression |
---|---|
rspct |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2311 | . . . 4 | |
2 | eleq1 2100 | . . . . . . . . . 10 | |
3 | 2 | adantr 261 | . . . . . . . . 9 |
4 | simpr 103 | . . . . . . . . 9 | |
5 | 3, 4 | imbi12d 223 | . . . . . . . 8 |
6 | 5 | ex 108 | . . . . . . 7 |
7 | 6 | a2i 11 | . . . . . 6 |
8 | 7 | alimi 1344 | . . . . 5 |
9 | nfv 1421 | . . . . . . 7 | |
10 | rspct.1 | . . . . . . 7 | |
11 | 9, 10 | nfim 1464 | . . . . . 6 |
12 | nfcv 2178 | . . . . . 6 | |
13 | 11, 12 | spcgft 2630 | . . . . 5 |
14 | 8, 13 | syl 14 | . . . 4 |
15 | 1, 14 | syl7bi 154 | . . 3 |
16 | 15 | com34 77 | . 2 |
17 | 16 | pm2.43d 44 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wceq 1243 wnf 1349 wcel 1393 wral 2306 |
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-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-v 2559 |
This theorem is referenced by: (None) |
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