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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 2613 | . . . 4 | |
3 | 1, 2 | syl 14 | . . 3 |
4 | ralxfr2d.2 | . . . . . . . 8 | |
5 | 4 | biimprd 156 | . . . . . . 7 |
6 | r19.23v 2469 | . . . . . . 7 | |
7 | 5, 6 | sylibr 132 | . . . . . 6 |
8 | 7 | r19.21bi 2449 | . . . . 5 |
9 | eleq1 2141 | . . . . 5 | |
10 | 8, 9 | mpbidi 149 | . . . 4 |
11 | 10 | exlimdv 1740 | . . 3 |
12 | 3, 11 | mpd 13 | . 2 |
13 | 4 | biimpa 290 | . 2 |
14 | ralxfr2d.3 | . 2 | |
15 | 12, 13, 14 | rexxfrd 4213 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wceq 1284 wex 1421 wcel 1433 wral 2348 wrex 2349 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 |
This theorem is referenced by: rexrn 5325 rexima 5415 |
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