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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 2744 | . . . 4 | |
3 | 1, 2 | syl 14 | . . 3 |
4 | ralxfr2d.2 | . . . . . . . 8 | |
5 | 4 | biimprd 157 | . . . . . . 7 |
6 | r19.23v 2579 | . . . . . . 7 | |
7 | 5, 6 | sylibr 133 | . . . . . 6 |
8 | 7 | r19.21bi 2558 | . . . . 5 |
9 | eleq1 2233 | . . . . 5 | |
10 | 8, 9 | mpbidi 150 | . . . 4 |
11 | 10 | exlimdv 1812 | . . 3 |
12 | 3, 11 | mpd 13 | . 2 |
13 | 4 | biimpa 294 | . 2 |
14 | ralxfr2d.3 | . 2 | |
15 | 12, 13, 14 | rexxfrd 4448 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1348 wex 1485 wcel 2141 wral 2448 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: rexrn 5633 rexima 5734 cnptopresti 13032 cnptoprest 13033 txrest 13070 |
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