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Mirrors > Home > ILE Home > Th. List > rexxfr2d | Unicode version |
Description: Transfer universal quantification from a variable to another variable contained in expression . (Contributed by Mario Carneiro, 20-Aug-2014.) (Proof shortened by Mario Carneiro, 19-Nov-2016.) |
Ref | Expression |
---|---|
ralxfr2d.1 | |
ralxfr2d.2 | |
ralxfr2d.3 |
Ref | Expression |
---|---|
rexxfr2d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralxfr2d.1 | . . . 4 | |
2 | elisset 2674 | . . . 4 | |
3 | 1, 2 | syl 14 | . . 3 |
4 | ralxfr2d.2 | . . . . . . . 8 | |
5 | 4 | biimprd 157 | . . . . . . 7 |
6 | r19.23v 2518 | . . . . . . 7 | |
7 | 5, 6 | sylibr 133 | . . . . . 6 |
8 | 7 | r19.21bi 2497 | . . . . 5 |
9 | eleq1 2180 | . . . . 5 | |
10 | 8, 9 | mpbidi 150 | . . . 4 |
11 | 10 | exlimdv 1775 | . . 3 |
12 | 3, 11 | mpd 13 | . 2 |
13 | 4 | biimpa 294 | . 2 |
14 | ralxfr2d.3 | . 2 | |
15 | 12, 13, 14 | rexxfrd 4354 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1316 wex 1453 wcel 1465 wral 2393 wrex 2394 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 |
This theorem is referenced by: rexrn 5525 rexima 5624 cnptopresti 12334 cnptoprest 12335 txrest 12372 |
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