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Mirrors > Home > ILE Home > Th. List > dfmpt2 | Unicode version |
Description: Alternate definition for the "maps to" notation df-mpt2 5537 (although it requires that be a set). (Contributed by NM, 19-Dec-2008.) (Revised by Mario Carneiro, 31-Aug-2015.) |
Ref | Expression |
---|---|
dfmpt2.1 |
Ref | Expression |
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dfmpt2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpt2mpts 5844 | . 2 | |
2 | vex 2604 | . . . . 5 | |
3 | 1stexg 5814 | . . . . 5 | |
4 | 2, 3 | ax-mp 7 | . . . 4 |
5 | 2ndexg 5815 | . . . . . 6 | |
6 | 2, 5 | ax-mp 7 | . . . . 5 |
7 | dfmpt2.1 | . . . . 5 | |
8 | 6, 7 | csbexa 3907 | . . . 4 |
9 | 4, 8 | csbexa 3907 | . . 3 |
10 | 9 | dfmpt 5361 | . 2 |
11 | nfcv 2219 | . . . . 5 | |
12 | nfcsb1v 2938 | . . . . 5 | |
13 | 11, 12 | nfop 3586 | . . . 4 |
14 | 13 | nfsn 3452 | . . 3 |
15 | nfcv 2219 | . . . . 5 | |
16 | nfcv 2219 | . . . . . 6 | |
17 | nfcsb1v 2938 | . . . . . 6 | |
18 | 16, 17 | nfcsb 2940 | . . . . 5 |
19 | 15, 18 | nfop 3586 | . . . 4 |
20 | 19 | nfsn 3452 | . . 3 |
21 | nfcv 2219 | . . 3 | |
22 | id 19 | . . . . 5 | |
23 | csbopeq1a 5834 | . . . . 5 | |
24 | 22, 23 | opeq12d 3578 | . . . 4 |
25 | 24 | sneqd 3411 | . . 3 |
26 | 14, 20, 21, 25 | iunxpf 4502 | . 2 |
27 | 1, 10, 26 | 3eqtri 2105 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1284 wcel 1433 cvv 2601 csb 2908 csn 3398 cop 3401 ciun 3678 cmpt 3839 cxp 4361 cfv 4922 cmpt2 5534 c1st 5785 c2nd 5786 |
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-13 1444 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 ax-un 4188 |
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-reu 2355 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-uni 3602 df-iun 3680 df-br 3786 df-opab 3840 df-mpt 3841 df-id 4048 df-xp 4369 df-rel 4370 df-cnv 4371 df-co 4372 df-dm 4373 df-rn 4374 df-iota 4887 df-fun 4924 df-fn 4925 df-f 4926 df-f1 4927 df-fo 4928 df-f1o 4929 df-fv 4930 df-oprab 5536 df-mpt2 5537 df-1st 5787 df-2nd 5788 |
This theorem is referenced by: (None) |
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