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Mirrors > Home > ILE Home > Th. List > isosolem | Unicode version |
Description: Lemma for isoso 5464. (Contributed by Stefan O'Rear, 16-Nov-2014.) |
Ref | Expression |
---|---|
isosolem |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isopolem 5461 | . . 3 | |
2 | df-3an 887 | . . . . . . 7 | |
3 | isof1o 5447 | . . . . . . . . . . 11 | |
4 | f1of 5126 | . . . . . . . . . . 11 | |
5 | ffvelrn 5300 | . . . . . . . . . . . . 13 | |
6 | 5 | ex 108 | . . . . . . . . . . . 12 |
7 | ffvelrn 5300 | . . . . . . . . . . . . 13 | |
8 | 7 | ex 108 | . . . . . . . . . . . 12 |
9 | ffvelrn 5300 | . . . . . . . . . . . . 13 | |
10 | 9 | ex 108 | . . . . . . . . . . . 12 |
11 | 6, 8, 10 | 3anim123d 1214 | . . . . . . . . . . 11 |
12 | 3, 4, 11 | 3syl 17 | . . . . . . . . . 10 |
13 | 12 | imp 115 | . . . . . . . . 9 |
14 | breq1 3767 | . . . . . . . . . . 11 | |
15 | breq1 3767 | . . . . . . . . . . . 12 | |
16 | 15 | orbi1d 705 | . . . . . . . . . . 11 |
17 | 14, 16 | imbi12d 223 | . . . . . . . . . 10 |
18 | breq2 3768 | . . . . . . . . . . 11 | |
19 | breq2 3768 | . . . . . . . . . . . 12 | |
20 | 19 | orbi2d 704 | . . . . . . . . . . 11 |
21 | 18, 20 | imbi12d 223 | . . . . . . . . . 10 |
22 | breq2 3768 | . . . . . . . . . . . 12 | |
23 | breq1 3767 | . . . . . . . . . . . 12 | |
24 | 22, 23 | orbi12d 707 | . . . . . . . . . . 11 |
25 | 24 | imbi2d 219 | . . . . . . . . . 10 |
26 | 17, 21, 25 | rspc3v 2665 | . . . . . . . . 9 |
27 | 13, 26 | syl 14 | . . . . . . . 8 |
28 | isorel 5448 | . . . . . . . . . 10 | |
29 | 28 | 3adantr3 1065 | . . . . . . . . 9 |
30 | isorel 5448 | . . . . . . . . . . 11 | |
31 | 30 | 3adantr2 1064 | . . . . . . . . . 10 |
32 | isorel 5448 | . . . . . . . . . . . 12 | |
33 | 32 | ancom2s 500 | . . . . . . . . . . 11 |
34 | 33 | 3adantr1 1063 | . . . . . . . . . 10 |
35 | 31, 34 | orbi12d 707 | . . . . . . . . 9 |
36 | 29, 35 | imbi12d 223 | . . . . . . . 8 |
37 | 27, 36 | sylibrd 158 | . . . . . . 7 |
38 | 2, 37 | sylan2br 272 | . . . . . 6 |
39 | 38 | anassrs 380 | . . . . 5 |
40 | 39 | ralrimdva 2399 | . . . 4 |
41 | 40 | ralrimdvva 2404 | . . 3 |
42 | 1, 41 | anim12d 318 | . 2 |
43 | df-iso 4034 | . 2 | |
44 | df-iso 4034 | . 2 | |
45 | 42, 43, 44 | 3imtr4g 194 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wo 629 w3a 885 wceq 1243 wcel 1393 wral 2306 class class class wbr 3764 wpo 4031 wor 4032 wf 4898 wf1o 4901 cfv 4902 wiso 4903 |
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-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-v 2559 df-sbc 2765 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-id 4030 df-po 4033 df-iso 4034 df-xp 4351 df-rel 4352 df-cnv 4353 df-co 4354 df-dm 4355 df-rn 4356 df-iota 4867 df-fun 4904 df-fn 4905 df-f 4906 df-f1 4907 df-f1o 4909 df-fv 4910 df-isom 4911 |
This theorem is referenced by: isoso 5464 |
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