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Mirrors > Home > ILE Home > Th. List > rexrnmpt2 | Unicode version |
Description: A restricted quantifier over an image set. (Contributed by Mario Carneiro, 1-Sep-2015.) |
Ref | Expression |
---|---|
rngop.1 | |
ralrnmpt2.2 |
Ref | Expression |
---|---|
rexrnmpt2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rngop.1 | . . . . 5 | |
2 | 1 | rnmpt2 5631 | . . . 4 |
3 | 2 | rexeqi 2554 | . . 3 |
4 | eqeq1 2087 | . . . . 5 | |
5 | 4 | 2rexbidv 2391 | . . . 4 |
6 | 5 | rexab 2754 | . . 3 |
7 | rexcom4 2622 | . . . 4 | |
8 | r19.41v 2510 | . . . . 5 | |
9 | 8 | exbii 1536 | . . . 4 |
10 | 7, 9 | bitr2i 183 | . . 3 |
11 | 3, 6, 10 | 3bitri 204 | . 2 |
12 | rexcom4 2622 | . . . . . 6 | |
13 | r19.41v 2510 | . . . . . . 7 | |
14 | 13 | exbii 1536 | . . . . . 6 |
15 | 12, 14 | bitri 182 | . . . . 5 |
16 | ralrnmpt2.2 | . . . . . . . 8 | |
17 | 16 | ceqsexgv 2724 | . . . . . . 7 |
18 | 17 | ralimi 2426 | . . . . . 6 |
19 | rexbi 2490 | . . . . . 6 | |
20 | 18, 19 | syl 14 | . . . . 5 |
21 | 15, 20 | syl5bbr 192 | . . . 4 |
22 | 21 | ralimi 2426 | . . 3 |
23 | rexbi 2490 | . . 3 | |
24 | 22, 23 | syl 14 | . 2 |
25 | 11, 24 | syl5bb 190 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wceq 1284 wex 1421 wcel 1433 cab 2067 wral 2348 wrex 2349 crn 4364 cmpt2 5534 |
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-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-br 3786 df-opab 3840 df-cnv 4371 df-dm 4373 df-rn 4374 df-oprab 5536 df-mpt2 5537 |
This theorem is referenced by: (None) |
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