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Mirrors > Home > ILE Home > Th. List > isosolem | Unicode version |
Description: Lemma for isoso 5787. (Contributed by Stefan O'Rear, 16-Nov-2014.) |
Ref | Expression |
---|---|
isosolem |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isopolem 5784 | . . 3 | |
2 | df-3an 969 | . . . . . . 7 | |
3 | isof1o 5769 | . . . . . . . . . . 11 | |
4 | f1of 5426 | . . . . . . . . . . 11 | |
5 | ffvelrn 5612 | . . . . . . . . . . . . 13 | |
6 | 5 | ex 114 | . . . . . . . . . . . 12 |
7 | ffvelrn 5612 | . . . . . . . . . . . . 13 | |
8 | 7 | ex 114 | . . . . . . . . . . . 12 |
9 | ffvelrn 5612 | . . . . . . . . . . . . 13 | |
10 | 9 | ex 114 | . . . . . . . . . . . 12 |
11 | 6, 8, 10 | 3anim123d 1308 | . . . . . . . . . . 11 |
12 | 3, 4, 11 | 3syl 17 | . . . . . . . . . 10 |
13 | 12 | imp 123 | . . . . . . . . 9 |
14 | breq1 3979 | . . . . . . . . . . 11 | |
15 | breq1 3979 | . . . . . . . . . . . 12 | |
16 | 15 | orbi1d 781 | . . . . . . . . . . 11 |
17 | 14, 16 | imbi12d 233 | . . . . . . . . . 10 |
18 | breq2 3980 | . . . . . . . . . . 11 | |
19 | breq2 3980 | . . . . . . . . . . . 12 | |
20 | 19 | orbi2d 780 | . . . . . . . . . . 11 |
21 | 18, 20 | imbi12d 233 | . . . . . . . . . 10 |
22 | breq2 3980 | . . . . . . . . . . . 12 | |
23 | breq1 3979 | . . . . . . . . . . . 12 | |
24 | 22, 23 | orbi12d 783 | . . . . . . . . . . 11 |
25 | 24 | imbi2d 229 | . . . . . . . . . 10 |
26 | 17, 21, 25 | rspc3v 2841 | . . . . . . . . 9 |
27 | 13, 26 | syl 14 | . . . . . . . 8 |
28 | isorel 5770 | . . . . . . . . . 10 | |
29 | 28 | 3adantr3 1147 | . . . . . . . . 9 |
30 | isorel 5770 | . . . . . . . . . . 11 | |
31 | 30 | 3adantr2 1146 | . . . . . . . . . 10 |
32 | isorel 5770 | . . . . . . . . . . . 12 | |
33 | 32 | ancom2s 556 | . . . . . . . . . . 11 |
34 | 33 | 3adantr1 1145 | . . . . . . . . . 10 |
35 | 31, 34 | orbi12d 783 | . . . . . . . . 9 |
36 | 29, 35 | imbi12d 233 | . . . . . . . 8 |
37 | 27, 36 | sylibrd 168 | . . . . . . 7 |
38 | 2, 37 | sylan2br 286 | . . . . . 6 |
39 | 38 | anassrs 398 | . . . . 5 |
40 | 39 | ralrimdva 2544 | . . . 4 |
41 | 40 | ralrimdvva 2549 | . . 3 |
42 | 1, 41 | anim12d 333 | . 2 |
43 | df-iso 4269 | . 2 | |
44 | df-iso 4269 | . 2 | |
45 | 42, 43, 44 | 3imtr4g 204 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wo 698 w3a 967 wceq 1342 wcel 2135 wral 2442 class class class wbr 3976 wpo 4266 wor 4267 wf 5178 wf1o 5181 cfv 5182 wiso 5183 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-sbc 2947 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-br 3977 df-opab 4038 df-id 4265 df-po 4268 df-iso 4269 df-xp 4604 df-rel 4605 df-cnv 4606 df-co 4607 df-dm 4608 df-rn 4609 df-iota 5147 df-fun 5184 df-fn 5185 df-f 5186 df-f1 5187 df-f1o 5189 df-fv 5190 df-isom 5191 |
This theorem is referenced by: isoso 5787 |
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