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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 1508 | . . . . 5 | |
2 | 1 | 19.3 1533 | . . . 4 |
3 | ralxfrd.2 | . . . . 5 | |
4 | df-rex 2420 | . . . . . . . 8 | |
5 | 19.29 1599 | . . . . . . . . . 10 | |
6 | an12 550 | . . . . . . . . . . 11 | |
7 | 6 | exbii 1584 | . . . . . . . . . 10 |
8 | 5, 7 | sylib 121 | . . . . . . . . 9 |
9 | df-rex 2420 | . . . . . . . . 9 | |
10 | 8, 9 | sylibr 133 | . . . . . . . 8 |
11 | 4, 10 | sylan2b 285 | . . . . . . 7 |
12 | ralxfrd.3 | . . . . . . . . . . 11 | |
13 | 12 | biimpd 143 | . . . . . . . . . 10 |
14 | 13 | expimpd 360 | . . . . . . . . 9 |
15 | 14 | ancomsd 267 | . . . . . . . 8 |
16 | 15 | reximdv 2531 | . . . . . . 7 |
17 | 11, 16 | syl5 32 | . . . . . 6 |
18 | 17 | adantr 274 | . . . . 5 |
19 | 3, 18 | mpan2d 424 | . . . 4 |
20 | 2, 19 | syl5bir 152 | . . 3 |
21 | 20 | rexlimdva 2547 | . 2 |
22 | ralxfrd.1 | . . . 4 | |
23 | 12 | adantlr 468 | . . . 4 |
24 | 22, 23 | rspcedv 2788 | . . 3 |
25 | 24 | rexlimdva 2547 | . 2 |
26 | 21, 25 | impbid 128 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1329 wceq 1331 wex 1468 wcel 1480 wrex 2415 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 |
This theorem is referenced by: rexxfr2d 4381 rexxfr 4384 |
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