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Mirrors > Home > ILE Home > Th. List > imadiflem | Unicode version |
Description: One direction of imadif 4979. This direction does not require . (Contributed by Jim Kingdon, 25-Dec-2018.) |
Ref | Expression |
---|---|
imadiflem |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2312 | . . . 4 | |
2 | df-rex 2312 | . . . . 5 | |
3 | 2 | notbii 594 | . . . 4 |
4 | alnex 1388 | . . . . . . 7 | |
5 | 19.29r 1512 | . . . . . . 7 | |
6 | 4, 5 | sylan2br 272 | . . . . . 6 |
7 | simpl 102 | . . . . . . . . 9 | |
8 | simplr 482 | . . . . . . . . . 10 | |
9 | simpr 103 | . . . . . . . . . . 11 | |
10 | ancom 253 | . . . . . . . . . . . . 13 | |
11 | 10 | notbii 594 | . . . . . . . . . . . 12 |
12 | imnan 624 | . . . . . . . . . . . 12 | |
13 | 11, 12 | bitr4i 176 | . . . . . . . . . . 11 |
14 | 9, 13 | sylib 127 | . . . . . . . . . 10 |
15 | 8, 14 | mpd 13 | . . . . . . . . 9 |
16 | 7, 15, 8 | jca32 293 | . . . . . . . 8 |
17 | eldif 2927 | . . . . . . . . . 10 | |
18 | 17 | anbi1i 431 | . . . . . . . . 9 |
19 | anandir 525 | . . . . . . . . 9 | |
20 | 18, 19 | bitri 173 | . . . . . . . 8 |
21 | 16, 20 | sylibr 137 | . . . . . . 7 |
22 | 21 | eximi 1491 | . . . . . 6 |
23 | 6, 22 | syl 14 | . . . . 5 |
24 | df-rex 2312 | . . . . 5 | |
25 | 23, 24 | sylibr 137 | . . . 4 |
26 | 1, 3, 25 | syl2anb 275 | . . 3 |
27 | 26 | ss2abi 3012 | . 2 |
28 | dfima2 4670 | . . . 4 | |
29 | dfima2 4670 | . . . 4 | |
30 | 28, 29 | difeq12i 3060 | . . 3 |
31 | difab 3206 | . . 3 | |
32 | 30, 31 | eqtri 2060 | . 2 |
33 | dfima2 4670 | . 2 | |
34 | 27, 32, 33 | 3sstr4i 2984 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wal 1241 wex 1381 wcel 1393 cab 2026 wrex 2307 cdif 2914 wss 2917 class class class wbr 3764 cima 4348 |
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-in1 544 ax-in2 545 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-fal 1249 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-dif 2920 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-br 3765 df-opab 3819 df-xp 4351 df-cnv 4353 df-dm 4355 df-rn 4356 df-res 4357 df-ima 4358 |
This theorem is referenced by: imadif 4979 |
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