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Mirrors > Home > ILE Home > Th. List > raliunxp | Unicode version |
Description: Write a double restricted quantification as one universal quantifier. In this version of ralxp 4754, is not assumed to be constant. (Contributed by Mario Carneiro, 29-Dec-2014.) |
Ref | Expression |
---|---|
ralxp.1 |
Ref | Expression |
---|---|
raliunxp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eliunxp 4750 | . . . . . 6 | |
2 | 1 | imbi1i 237 | . . . . 5 |
3 | 19.23vv 1877 | . . . . 5 | |
4 | 2, 3 | bitr4i 186 | . . . 4 |
5 | 4 | albii 1463 | . . 3 |
6 | alrot3 1478 | . . . 4 | |
7 | impexp 261 | . . . . . . 7 | |
8 | 7 | albii 1463 | . . . . . 6 |
9 | vex 2733 | . . . . . . . 8 | |
10 | vex 2733 | . . . . . . . 8 | |
11 | 9, 10 | opex 4214 | . . . . . . 7 |
12 | ralxp.1 | . . . . . . . 8 | |
13 | 12 | imbi2d 229 | . . . . . . 7 |
14 | 11, 13 | ceqsalv 2760 | . . . . . 6 |
15 | 8, 14 | bitri 183 | . . . . 5 |
16 | 15 | 2albii 1464 | . . . 4 |
17 | 6, 16 | bitri 183 | . . 3 |
18 | 5, 17 | bitri 183 | . 2 |
19 | df-ral 2453 | . 2 | |
20 | r2al 2489 | . 2 | |
21 | 18, 19, 20 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1346 wceq 1348 wex 1485 wcel 2141 wral 2448 csn 3583 cop 3586 ciun 3873 cxp 4609 |
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-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 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 df-sbc 2956 df-csb 3050 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-iun 3875 df-opab 4051 df-xp 4617 df-rel 4618 |
This theorem is referenced by: ralxp 4754 fmpox 6179 |
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