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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 4730, 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 4726 | . . . . . 6 | |
2 | 1 | imbi1i 237 | . . . . 5 |
3 | 19.23vv 1864 | . . . . 5 | |
4 | 2, 3 | bitr4i 186 | . . . 4 |
5 | 4 | albii 1450 | . . 3 |
6 | alrot3 1465 | . . . 4 | |
7 | impexp 261 | . . . . . . 7 | |
8 | 7 | albii 1450 | . . . . . 6 |
9 | vex 2715 | . . . . . . . 8 | |
10 | vex 2715 | . . . . . . . 8 | |
11 | 9, 10 | opex 4190 | . . . . . . 7 |
12 | ralxp.1 | . . . . . . . 8 | |
13 | 12 | imbi2d 229 | . . . . . . 7 |
14 | 11, 13 | ceqsalv 2742 | . . . . . 6 |
15 | 8, 14 | bitri 183 | . . . . 5 |
16 | 15 | 2albii 1451 | . . . 4 |
17 | 6, 16 | bitri 183 | . . 3 |
18 | 5, 17 | bitri 183 | . 2 |
19 | df-ral 2440 | . 2 | |
20 | r2al 2476 | . 2 | |
21 | 18, 19, 20 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1333 wceq 1335 wex 1472 wcel 2128 wral 2435 csn 3560 cop 3563 ciun 3850 cxp 4585 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4083 ax-pow 4136 ax-pr 4170 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-sbc 2938 df-csb 3032 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-iun 3852 df-opab 4027 df-xp 4593 df-rel 4594 |
This theorem is referenced by: ralxp 4730 fmpox 6149 |
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