Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > rspcimdv | Unicode version |
Description: Restricted specialization, using implicit substitution. (Contributed by Mario Carneiro, 4-Jan-2017.) |
Ref | Expression |
---|---|
rspcimdv.1 | |
rspcimdv.2 |
Ref | Expression |
---|---|
rspcimdv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2353 | . 2 | |
2 | rspcimdv.1 | . . 3 | |
3 | simpr 108 | . . . . . . 7 | |
4 | 3 | eleq1d 2147 | . . . . . 6 |
5 | 4 | biimprd 156 | . . . . 5 |
6 | rspcimdv.2 | . . . . 5 | |
7 | 5, 6 | imim12d 73 | . . . 4 |
8 | 2, 7 | spcimdv 2682 | . . 3 |
9 | 2, 8 | mpid 41 | . 2 |
10 | 1, 9 | syl5bi 150 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wal 1282 wceq 1284 wcel 1433 wral 2348 |
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-ral 2353 df-v 2603 |
This theorem is referenced by: rspcdv 2704 |
Copyright terms: Public domain | W3C validator |