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Mirrors > Home > ILE Home > Th. List > isosolem | Unicode version |
Description: Lemma for isoso 5484. (Contributed by Stefan O'Rear, 16-Nov-2014.) |
Ref | Expression |
---|---|
isosolem |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isopolem 5481 | . . 3 | |
2 | df-3an 921 | . . . . . . 7 | |
3 | isof1o 5467 | . . . . . . . . . . 11 | |
4 | f1of 5146 | . . . . . . . . . . 11 | |
5 | ffvelrn 5321 | . . . . . . . . . . . . 13 | |
6 | 5 | ex 113 | . . . . . . . . . . . 12 |
7 | ffvelrn 5321 | . . . . . . . . . . . . 13 | |
8 | 7 | ex 113 | . . . . . . . . . . . 12 |
9 | ffvelrn 5321 | . . . . . . . . . . . . 13 | |
10 | 9 | ex 113 | . . . . . . . . . . . 12 |
11 | 6, 8, 10 | 3anim123d 1250 | . . . . . . . . . . 11 |
12 | 3, 4, 11 | 3syl 17 | . . . . . . . . . 10 |
13 | 12 | imp 122 | . . . . . . . . 9 |
14 | breq1 3788 | . . . . . . . . . . 11 | |
15 | breq1 3788 | . . . . . . . . . . . 12 | |
16 | 15 | orbi1d 737 | . . . . . . . . . . 11 |
17 | 14, 16 | imbi12d 232 | . . . . . . . . . 10 |
18 | breq2 3789 | . . . . . . . . . . 11 | |
19 | breq2 3789 | . . . . . . . . . . . 12 | |
20 | 19 | orbi2d 736 | . . . . . . . . . . 11 |
21 | 18, 20 | imbi12d 232 | . . . . . . . . . 10 |
22 | breq2 3789 | . . . . . . . . . . . 12 | |
23 | breq1 3788 | . . . . . . . . . . . 12 | |
24 | 22, 23 | orbi12d 739 | . . . . . . . . . . 11 |
25 | 24 | imbi2d 228 | . . . . . . . . . 10 |
26 | 17, 21, 25 | rspc3v 2716 | . . . . . . . . 9 |
27 | 13, 26 | syl 14 | . . . . . . . 8 |
28 | isorel 5468 | . . . . . . . . . 10 | |
29 | 28 | 3adantr3 1099 | . . . . . . . . 9 |
30 | isorel 5468 | . . . . . . . . . . 11 | |
31 | 30 | 3adantr2 1098 | . . . . . . . . . 10 |
32 | isorel 5468 | . . . . . . . . . . . 12 | |
33 | 32 | ancom2s 530 | . . . . . . . . . . 11 |
34 | 33 | 3adantr1 1097 | . . . . . . . . . 10 |
35 | 31, 34 | orbi12d 739 | . . . . . . . . 9 |
36 | 29, 35 | imbi12d 232 | . . . . . . . 8 |
37 | 27, 36 | sylibrd 167 | . . . . . . 7 |
38 | 2, 37 | sylan2br 282 | . . . . . 6 |
39 | 38 | anassrs 392 | . . . . 5 |
40 | 39 | ralrimdva 2441 | . . . 4 |
41 | 40 | ralrimdvva 2446 | . . 3 |
42 | 1, 41 | anim12d 328 | . 2 |
43 | df-iso 4052 | . 2 | |
44 | df-iso 4052 | . 2 | |
45 | 42, 43, 44 | 3imtr4g 203 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wo 661 w3a 919 wceq 1284 wcel 1433 wral 2348 class class class wbr 3785 wpo 4049 wor 4050 wf 4918 wf1o 4921 cfv 4922 wiso 4923 |
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-in1 576 ax-in2 577 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-eu 1944 df-mo 1945 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-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-br 3786 df-opab 3840 df-id 4048 df-po 4051 df-iso 4052 df-xp 4369 df-rel 4370 df-cnv 4371 df-co 4372 df-dm 4373 df-rn 4374 df-iota 4887 df-fun 4924 df-fn 4925 df-f 4926 df-f1 4927 df-f1o 4929 df-fv 4930 df-isom 4931 |
This theorem is referenced by: isoso 5484 |
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