Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > mpt2mptx | 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 |
---|---|
mpt2mpt.1 |
Ref | Expression |
---|---|
mpt2mptx |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-mpt 3820 | . 2 | |
2 | df-mpt2 5517 | . . 3 | |
3 | eliunxp 4475 | . . . . . . 7 | |
4 | 3 | anbi1i 431 | . . . . . 6 |
5 | 19.41vv 1783 | . . . . . 6 | |
6 | anass 381 | . . . . . . . 8 | |
7 | mpt2mpt.1 | . . . . . . . . . . 11 | |
8 | 7 | eqeq2d 2051 | . . . . . . . . . 10 |
9 | 8 | anbi2d 437 | . . . . . . . . 9 |
10 | 9 | pm5.32i 427 | . . . . . . . 8 |
11 | 6, 10 | bitri 173 | . . . . . . 7 |
12 | 11 | 2exbii 1497 | . . . . . 6 |
13 | 4, 5, 12 | 3bitr2i 197 | . . . . 5 |
14 | 13 | opabbii 3824 | . . . 4 |
15 | dfoprab2 5552 | . . . 4 | |
16 | 14, 15 | eqtr4i 2063 | . . 3 |
17 | 2, 16 | eqtr4i 2063 | . 2 |
18 | 1, 17 | eqtr4i 2063 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wceq 1243 wex 1381 wcel 1393 csn 3375 cop 3378 ciun 3657 copab 3817 cmpt 3818 cxp 4343 coprab 5513 cmpt2 5514 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-sbc 2765 df-csb 2853 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-iun 3659 df-opab 3819 df-mpt 3820 df-xp 4351 df-rel 4352 df-oprab 5516 df-mpt2 5517 |
This theorem is referenced by: mpt2mpt 5596 mpt2mptsx 5823 dmmpt2ssx 5825 fmpt2x 5826 |
Copyright terms: Public domain | W3C validator |