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Mirrors > Home > ILE Home > Th. List > dfmpo | Unicode version |
Description: Alternate definition for the maps-to notation df-mpo 5858 (although it requires that be a set). (Contributed by NM, 19-Dec-2008.) (Revised by Mario Carneiro, 31-Aug-2015.) |
Ref | Expression |
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dfmpo.1 |
Ref | Expression |
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dfmpo |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpompts 6177 | . 2 | |
2 | vex 2733 | . . . . 5 | |
3 | 1stexg 6146 | . . . . 5 | |
4 | 2, 3 | ax-mp 5 | . . . 4 |
5 | 2ndexg 6147 | . . . . . 6 | |
6 | 2, 5 | ax-mp 5 | . . . . 5 |
7 | dfmpo.1 | . . . . 5 | |
8 | 6, 7 | csbexa 4118 | . . . 4 |
9 | 4, 8 | csbexa 4118 | . . 3 |
10 | 9 | dfmpt 5673 | . 2 |
11 | nfcv 2312 | . . . . 5 | |
12 | nfcsb1v 3082 | . . . . 5 | |
13 | 11, 12 | nfop 3781 | . . . 4 |
14 | 13 | nfsn 3643 | . . 3 |
15 | nfcv 2312 | . . . . 5 | |
16 | nfcv 2312 | . . . . . 6 | |
17 | nfcsb1v 3082 | . . . . . 6 | |
18 | 16, 17 | nfcsb 3086 | . . . . 5 |
19 | 15, 18 | nfop 3781 | . . . 4 |
20 | 19 | nfsn 3643 | . . 3 |
21 | nfcv 2312 | . . 3 | |
22 | id 19 | . . . . 5 | |
23 | csbopeq1a 6167 | . . . . 5 | |
24 | 22, 23 | opeq12d 3773 | . . . 4 |
25 | 24 | sneqd 3596 | . . 3 |
26 | 14, 20, 21, 25 | iunxpf 4759 | . 2 |
27 | 1, 10, 26 | 3eqtri 2195 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1348 wcel 2141 cvv 2730 csb 3049 csn 3583 cop 3586 ciun 3873 cmpt 4050 cxp 4609 cfv 5198 cmpo 5855 c1st 6117 c2nd 6118 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-13 2143 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 ax-un 4418 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-reu 2455 df-v 2732 df-sbc 2956 df-csb 3050 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-uni 3797 df-iun 3875 df-br 3990 df-opab 4051 df-mpt 4052 df-id 4278 df-xp 4617 df-rel 4618 df-cnv 4619 df-co 4620 df-dm 4621 df-rn 4622 df-iota 5160 df-fun 5200 df-fn 5201 df-f 5202 df-f1 5203 df-fo 5204 df-f1o 5205 df-fv 5206 df-oprab 5857 df-mpo 5858 df-1st 6119 df-2nd 6120 |
This theorem is referenced by: (None) |
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