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Mirrors > Home > ILE Home > Th. List > mpomptx | Unicode version |
Description: Express a two-argument function as a one-argument function, or vice-versa. In this version is not assumed to be constant w.r.t . (Contributed by Mario Carneiro, 29-Dec-2014.) |
Ref | Expression |
---|---|
mpompt.1 |
Ref | Expression |
---|---|
mpomptx |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-mpt 3991 | . 2 | |
2 | df-mpo 5779 | . . 3 | |
3 | eliunxp 4678 | . . . . . . 7 | |
4 | 3 | anbi1i 453 | . . . . . 6 |
5 | 19.41vv 1875 | . . . . . 6 | |
6 | anass 398 | . . . . . . . 8 | |
7 | mpompt.1 | . . . . . . . . . . 11 | |
8 | 7 | eqeq2d 2151 | . . . . . . . . . 10 |
9 | 8 | anbi2d 459 | . . . . . . . . 9 |
10 | 9 | pm5.32i 449 | . . . . . . . 8 |
11 | 6, 10 | bitri 183 | . . . . . . 7 |
12 | 11 | 2exbii 1585 | . . . . . 6 |
13 | 4, 5, 12 | 3bitr2i 207 | . . . . 5 |
14 | 13 | opabbii 3995 | . . . 4 |
15 | dfoprab2 5818 | . . . 4 | |
16 | 14, 15 | eqtr4i 2163 | . . 3 |
17 | 2, 16 | eqtr4i 2163 | . 2 |
18 | 1, 17 | eqtr4i 2163 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1331 wex 1468 wcel 1480 csn 3527 cop 3530 ciun 3813 copab 3988 cmpt 3989 cxp 4537 coprab 5775 cmpo 5776 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-sbc 2910 df-csb 3004 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-iun 3815 df-opab 3990 df-mpt 3991 df-xp 4545 df-rel 4546 df-oprab 5778 df-mpo 5779 |
This theorem is referenced by: mpompt 5863 mpomptsx 6095 dmmpossx 6097 fmpox 6098 |
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