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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 4498, 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 4493 | . . . . . 6 | |
2 | 1 | anbi1i 445 | . . . . 5 |
3 | 19.41vv 1824 | . . . . 5 | |
4 | 2, 3 | bitr4i 185 | . . . 4 |
5 | 4 | exbii 1536 | . . 3 |
6 | exrot3 1620 | . . . 4 | |
7 | anass 393 | . . . . . . 7 | |
8 | 7 | exbii 1536 | . . . . . 6 |
9 | vex 2604 | . . . . . . . 8 | |
10 | vex 2604 | . . . . . . . 8 | |
11 | 9, 10 | opex 3984 | . . . . . . 7 |
12 | ralxp.1 | . . . . . . . 8 | |
13 | 12 | anbi2d 451 | . . . . . . 7 |
14 | 11, 13 | ceqsexv 2638 | . . . . . 6 |
15 | 8, 14 | bitri 182 | . . . . 5 |
16 | 15 | 2exbii 1537 | . . . 4 |
17 | 6, 16 | bitri 182 | . . 3 |
18 | 5, 17 | bitri 182 | . 2 |
19 | df-rex 2354 | . 2 | |
20 | r2ex 2386 | . 2 | |
21 | 18, 19, 20 | 3bitr4i 210 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wceq 1284 wex 1421 wcel 1433 wrex 2349 csn 3398 cop 3401 ciun 3678 cxp 4361 |
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-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 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 df-sbc 2816 df-csb 2909 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-iun 3680 df-opab 3840 df-xp 4369 df-rel 4370 |
This theorem is referenced by: rexxp 4498 |
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