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Mirrors > Home > ILE Home > Th. List > f1mpt | Unicode version |
Description: Express injection for a mapping operation. (Contributed by Mario Carneiro, 2-Jan-2017.) |
Ref | Expression |
---|---|
f1mpt.1 | |
f1mpt.2 |
Ref | Expression |
---|---|
f1mpt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1mpt.1 | . . . 4 | |
2 | nfmpt1 3850 | . . . 4 | |
3 | 1, 2 | nfcxfr 2175 | . . 3 |
4 | nfcv 2178 | . . 3 | |
5 | 3, 4 | dff13f 5409 | . 2 |
6 | 1 | fmpt 5319 | . . 3 |
7 | 6 | anbi1i 431 | . 2 |
8 | f1mpt.2 | . . . . . . 7 | |
9 | 8 | eleq1d 2106 | . . . . . 6 |
10 | 9 | cbvralv 2533 | . . . . 5 |
11 | raaanv 3328 | . . . . . 6 | |
12 | 1 | fvmpt2 5254 | . . . . . . . . . . . . . 14 |
13 | 8, 1 | fvmptg 5248 | . . . . . . . . . . . . . 14 |
14 | 12, 13 | eqeqan12d 2055 | . . . . . . . . . . . . 13 |
15 | 14 | an4s 522 | . . . . . . . . . . . 12 |
16 | 15 | imbi1d 220 | . . . . . . . . . . 11 |
17 | 16 | ex 108 | . . . . . . . . . 10 |
18 | 17 | ralimdva 2387 | . . . . . . . . 9 |
19 | ralbi 2445 | . . . . . . . . 9 | |
20 | 18, 19 | syl6 29 | . . . . . . . 8 |
21 | 20 | ralimia 2382 | . . . . . . 7 |
22 | ralbi 2445 | . . . . . . 7 | |
23 | 21, 22 | syl 14 | . . . . . 6 |
24 | 11, 23 | sylbir 125 | . . . . 5 |
25 | 10, 24 | sylan2b 271 | . . . 4 |
26 | 25 | anidms 377 | . . 3 |
27 | 26 | pm5.32i 427 | . 2 |
28 | 5, 7, 27 | 3bitr2i 197 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wceq 1243 wcel 1393 wral 2306 cmpt 3818 wf 4898 wf1 4899 cfv 4902 |
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-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-rab 2315 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-uni 3581 df-br 3765 df-opab 3819 df-mpt 3820 df-id 4030 df-xp 4351 df-rel 4352 df-cnv 4353 df-co 4354 df-dm 4355 df-rn 4356 df-res 4357 df-ima 4358 df-iota 4867 df-fun 4904 df-fn 4905 df-f 4906 df-f1 4907 df-fv 4910 |
This theorem is referenced by: (None) |
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