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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 1521 | . . . . 5 | |
2 | 1 | 19.3 1547 | . . . 4 |
3 | ralxfrd.2 | . . . . 5 | |
4 | df-rex 2454 | . . . . . . . 8 | |
5 | 19.29 1613 | . . . . . . . . . 10 | |
6 | an12 556 | . . . . . . . . . . 11 | |
7 | 6 | exbii 1598 | . . . . . . . . . 10 |
8 | 5, 7 | sylib 121 | . . . . . . . . 9 |
9 | df-rex 2454 | . . . . . . . . 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 361 | . . . . . . . . 9 |
15 | 14 | ancomsd 267 | . . . . . . . 8 |
16 | 15 | reximdv 2571 | . . . . . . 7 |
17 | 11, 16 | syl5 32 | . . . . . 6 |
18 | 17 | adantr 274 | . . . . 5 |
19 | 3, 18 | mpan2d 426 | . . . 4 |
20 | 2, 19 | syl5bir 152 | . . 3 |
21 | 20 | rexlimdva 2587 | . 2 |
22 | ralxfrd.1 | . . . 4 | |
23 | 12 | adantlr 474 | . . . 4 |
24 | 22, 23 | rspcedv 2838 | . . 3 |
25 | 24 | rexlimdva 2587 | . 2 |
26 | 21, 25 | impbid 128 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1346 wceq 1348 wex 1485 wcel 2141 wrex 2449 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 |
This theorem is referenced by: rexxfr2d 4448 rexxfr 4451 |
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