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Mirrors > Home > ILE Home > Th. List > isosolem | Unicode version |
Description: Lemma for isoso 5726. (Contributed by Stefan O'Rear, 16-Nov-2014.) |
Ref | Expression |
---|---|
isosolem |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isopolem 5723 | . . 3 | |
2 | df-3an 964 | . . . . . . 7 | |
3 | isof1o 5708 | . . . . . . . . . . 11 | |
4 | f1of 5367 | . . . . . . . . . . 11 | |
5 | ffvelrn 5553 | . . . . . . . . . . . . 13 | |
6 | 5 | ex 114 | . . . . . . . . . . . 12 |
7 | ffvelrn 5553 | . . . . . . . . . . . . 13 | |
8 | 7 | ex 114 | . . . . . . . . . . . 12 |
9 | ffvelrn 5553 | . . . . . . . . . . . . 13 | |
10 | 9 | ex 114 | . . . . . . . . . . . 12 |
11 | 6, 8, 10 | 3anim123d 1297 | . . . . . . . . . . 11 |
12 | 3, 4, 11 | 3syl 17 | . . . . . . . . . 10 |
13 | 12 | imp 123 | . . . . . . . . 9 |
14 | breq1 3932 | . . . . . . . . . . 11 | |
15 | breq1 3932 | . . . . . . . . . . . 12 | |
16 | 15 | orbi1d 780 | . . . . . . . . . . 11 |
17 | 14, 16 | imbi12d 233 | . . . . . . . . . 10 |
18 | breq2 3933 | . . . . . . . . . . 11 | |
19 | breq2 3933 | . . . . . . . . . . . 12 | |
20 | 19 | orbi2d 779 | . . . . . . . . . . 11 |
21 | 18, 20 | imbi12d 233 | . . . . . . . . . 10 |
22 | breq2 3933 | . . . . . . . . . . . 12 | |
23 | breq1 3932 | . . . . . . . . . . . 12 | |
24 | 22, 23 | orbi12d 782 | . . . . . . . . . . 11 |
25 | 24 | imbi2d 229 | . . . . . . . . . 10 |
26 | 17, 21, 25 | rspc3v 2805 | . . . . . . . . 9 |
27 | 13, 26 | syl 14 | . . . . . . . 8 |
28 | isorel 5709 | . . . . . . . . . 10 | |
29 | 28 | 3adantr3 1142 | . . . . . . . . 9 |
30 | isorel 5709 | . . . . . . . . . . 11 | |
31 | 30 | 3adantr2 1141 | . . . . . . . . . 10 |
32 | isorel 5709 | . . . . . . . . . . . 12 | |
33 | 32 | ancom2s 555 | . . . . . . . . . . 11 |
34 | 33 | 3adantr1 1140 | . . . . . . . . . 10 |
35 | 31, 34 | orbi12d 782 | . . . . . . . . 9 |
36 | 29, 35 | imbi12d 233 | . . . . . . . 8 |
37 | 27, 36 | sylibrd 168 | . . . . . . 7 |
38 | 2, 37 | sylan2br 286 | . . . . . 6 |
39 | 38 | anassrs 397 | . . . . 5 |
40 | 39 | ralrimdva 2512 | . . . 4 |
41 | 40 | ralrimdvva 2517 | . . 3 |
42 | 1, 41 | anim12d 333 | . 2 |
43 | df-iso 4219 | . 2 | |
44 | df-iso 4219 | . 2 | |
45 | 42, 43, 44 | 3imtr4g 204 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wo 697 w3a 962 wceq 1331 wcel 1480 wral 2416 class class class wbr 3929 wpo 4216 wor 4217 wf 5119 wf1o 5122 cfv 5123 wiso 5124 |
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 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-sbc 2910 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-opab 3990 df-id 4215 df-po 4218 df-iso 4219 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-rn 4550 df-iota 5088 df-fun 5125 df-fn 5126 df-f 5127 df-f1 5128 df-f1o 5130 df-fv 5131 df-isom 5132 |
This theorem is referenced by: isoso 5726 |
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