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Mirrors > Home > ILE Home > Th. List > rexxfrd | Unicode version |
Description: Transfer universal quantification from a variable to another variable contained in expression . (Contributed by FL, 10-Apr-2007.) (Revised by Mario Carneiro, 15-Aug-2014.) |
Ref | Expression |
---|---|
ralxfrd.1 | |
ralxfrd.2 | |
ralxfrd.3 |
Ref | Expression |
---|---|
rexxfrd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1421 | . . . . 5 | |
2 | 1 | 19.3 1446 | . . . 4 |
3 | ralxfrd.2 | . . . . 5 | |
4 | df-rex 2312 | . . . . . . . 8 | |
5 | 19.29 1511 | . . . . . . . . . 10 | |
6 | an12 495 | . . . . . . . . . . 11 | |
7 | 6 | exbii 1496 | . . . . . . . . . 10 |
8 | 5, 7 | sylib 127 | . . . . . . . . 9 |
9 | df-rex 2312 | . . . . . . . . 9 | |
10 | 8, 9 | sylibr 137 | . . . . . . . 8 |
11 | 4, 10 | sylan2b 271 | . . . . . . 7 |
12 | ralxfrd.3 | . . . . . . . . . . 11 | |
13 | 12 | biimpd 132 | . . . . . . . . . 10 |
14 | 13 | expimpd 345 | . . . . . . . . 9 |
15 | 14 | ancomsd 256 | . . . . . . . 8 |
16 | 15 | reximdv 2420 | . . . . . . 7 |
17 | 11, 16 | syl5 28 | . . . . . 6 |
18 | 17 | adantr 261 | . . . . 5 |
19 | 3, 18 | mpan2d 404 | . . . 4 |
20 | 2, 19 | syl5bir 142 | . . 3 |
21 | 20 | rexlimdva 2433 | . 2 |
22 | ralxfrd.1 | . . . 4 | |
23 | 12 | adantlr 446 | . . . 4 |
24 | 22, 23 | rspcedv 2660 | . . 3 |
25 | 24 | rexlimdva 2433 | . 2 |
26 | 21, 25 | impbid 120 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wceq 1243 wex 1381 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-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 |
This theorem is referenced by: rexxfr2d 4197 rexxfr 4200 |
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