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Mirrors > Home > ILE Home > Th. List > mpt2mpt | Unicode version |
Description: Express a two-argument function as a one-argument function, or vice-versa. (Contributed by Mario Carneiro, 17-Dec-2013.) (Revised by Mario Carneiro, 29-Dec-2014.) |
Ref | Expression |
---|---|
mpt2mpt.1 |
Ref | Expression |
---|---|
mpt2mpt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iunxpconst 4418 | . . 3 | |
2 | mpteq1 3862 | . . 3 | |
3 | 1, 2 | ax-mp 7 | . 2 |
4 | mpt2mpt.1 | . . 3 | |
5 | 4 | mpt2mptx 5615 | . 2 |
6 | 3, 5 | eqtr3i 2103 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1284 csn 3398 cop 3401 ciun 3678 cmpt 3839 cxp 4361 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-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-mpt 3841 df-xp 4369 df-rel 4370 df-oprab 5536 df-mpt2 5537 |
This theorem is referenced by: fnovim 5629 fmpt2co 5857 |
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