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Mirrors > Home > ILE Home > Th. List > rexiunxp | Unicode version |
Description: Write a double restricted quantification as one universal quantifier. In this version of rexxp 4480, is not assumed to be constant. (Contributed by Mario Carneiro, 14-Feb-2015.) |
Ref | Expression |
---|---|
ralxp.1 |
Ref | Expression |
---|---|
rexiunxp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eliunxp 4475 | . . . . . 6 | |
2 | 1 | anbi1i 431 | . . . . 5 |
3 | 19.41vv 1783 | . . . . 5 | |
4 | 2, 3 | bitr4i 176 | . . . 4 |
5 | 4 | exbii 1496 | . . 3 |
6 | exrot3 1580 | . . . 4 | |
7 | anass 381 | . . . . . . 7 | |
8 | 7 | exbii 1496 | . . . . . 6 |
9 | vex 2560 | . . . . . . . 8 | |
10 | vex 2560 | . . . . . . . 8 | |
11 | 9, 10 | opex 3966 | . . . . . . 7 |
12 | ralxp.1 | . . . . . . . 8 | |
13 | 12 | anbi2d 437 | . . . . . . 7 |
14 | 11, 13 | ceqsexv 2593 | . . . . . 6 |
15 | 8, 14 | bitri 173 | . . . . 5 |
16 | 15 | 2exbii 1497 | . . . 4 |
17 | 6, 16 | bitri 173 | . . 3 |
18 | 5, 17 | bitri 173 | . 2 |
19 | df-rex 2312 | . 2 | |
20 | r2ex 2344 | . 2 | |
21 | 18, 19, 20 | 3bitr4i 201 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wceq 1243 wex 1381 wcel 1393 wrex 2307 csn 3375 cop 3378 ciun 3657 cxp 4343 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-sbc 2765 df-csb 2853 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-iun 3659 df-opab 3819 df-xp 4351 df-rel 4352 |
This theorem is referenced by: rexxp 4480 |
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