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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-rspgt | Unicode version |
Description: Restricted specialization, generalized. Weakens a hypothesis of rspccv 2653 and seems to have a shorter proof. (Contributed by BJ, 21-Nov-2019.) |
Ref | Expression |
---|---|
bj-rspg.nfa | |
bj-rspg.nfb | |
bj-rspg.nf2 |
Ref | Expression |
---|---|
bj-rspgt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2100 | . . . . . . . . 9 | |
2 | 1 | imbi1d 220 | . . . . . . . 8 |
3 | 2 | biimpd 132 | . . . . . . 7 |
4 | imim2 49 | . . . . . . . 8 | |
5 | 4 | imim2d 48 | . . . . . . 7 |
6 | 3, 5 | syl9 66 | . . . . . 6 |
7 | 6 | a2i 11 | . . . . 5 |
8 | 7 | alimi 1344 | . . . 4 |
9 | bj-rspg.nfa | . . . . 5 | |
10 | bj-rspg.nfb | . . . . . . 7 | |
11 | 9, 10 | nfel 2186 | . . . . . 6 |
12 | nfra1 2355 | . . . . . . 7 | |
13 | bj-rspg.nf2 | . . . . . . 7 | |
14 | 12, 13 | nfim 1464 | . . . . . 6 |
15 | 11, 14 | nfim 1464 | . . . . 5 |
16 | rsp 2369 | . . . . . . 7 | |
17 | 16 | a1i 9 | . . . . . 6 |
18 | 17 | com23 72 | . . . . 5 |
19 | 9, 15, 18 | bj-vtoclgft 9914 | . . . 4 |
20 | 8, 19 | syl 14 | . . 3 |
21 | 20 | pm2.43d 44 | . 2 |
22 | 21 | com23 72 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1241 wceq 1243 wnf 1349 wcel 1393 wnfc 2165 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: bj-rspg 9926 |
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