Step | Hyp | Ref
| Expression |
1 | | mhmrcl2 17339 |
. . 3
MndHom
|
2 | | mhmrcl1 17338 |
. . 3
MndHom
|
3 | 1, 2 | anim12ci 591 |
. 2
MndHom MndHom
|
4 | | eqid 2622 |
. . . . 5
|
5 | | eqid 2622 |
. . . . 5
|
6 | 4, 5 | mhmf 17340 |
. . . 4
MndHom
|
7 | | eqid 2622 |
. . . . 5
|
8 | 7, 4 | mhmf 17340 |
. . . 4
MndHom
|
9 | | fco 6058 |
. . . 4
|
10 | 6, 8, 9 | syl2an 494 |
. . 3
MndHom MndHom
|
11 | | eqid 2622 |
. . . . . . . . . 10
|
12 | | eqid 2622 |
. . . . . . . . . 10
|
13 | 7, 11, 12 | mhmlin 17342 |
. . . . . . . . 9
MndHom
|
14 | 13 | 3expb 1266 |
. . . . . . . 8
MndHom |
15 | 14 | adantll 750 |
. . . . . . 7
MndHom
MndHom |
16 | 15 | fveq2d 6195 |
. . . . . 6
MndHom
MndHom
|
17 | | simpll 790 |
. . . . . . 7
MndHom
MndHom
MndHom |
18 | 8 | ad2antlr 763 |
. . . . . . . 8
MndHom
MndHom |
19 | | simprl 794 |
. . . . . . . 8
MndHom
MndHom
|
20 | 18, 19 | ffvelrnd 6360 |
. . . . . . 7
MndHom
MndHom |
21 | | simprr 796 |
. . . . . . . 8
MndHom
MndHom |
22 | 18, 21 | ffvelrnd 6360 |
. . . . . . 7
MndHom
MndHom |
23 | | eqid 2622 |
. . . . . . . 8
|
24 | 4, 12, 23 | mhmlin 17342 |
. . . . . . 7
MndHom
|
25 | 17, 20, 22, 24 | syl3anc 1326 |
. . . . . 6
MndHom
MndHom |
26 | 16, 25 | eqtrd 2656 |
. . . . 5
MndHom
MndHom
|
27 | 2 | adantl 482 |
. . . . . . 7
MndHom MndHom
|
28 | 7, 11 | mndcl 17301 |
. . . . . . . 8
|
29 | 28 | 3expb 1266 |
. . . . . . 7
|
30 | 27, 29 | sylan 488 |
. . . . . 6
MndHom
MndHom |
31 | | fvco3 6275 |
. . . . . 6
|
32 | 18, 30, 31 | syl2anc 693 |
. . . . 5
MndHom
MndHom |
33 | | fvco3 6275 |
. . . . . . 7
|
34 | 18, 19, 33 | syl2anc 693 |
. . . . . 6
MndHom
MndHom |
35 | | fvco3 6275 |
. . . . . . 7
|
36 | 18, 21, 35 | syl2anc 693 |
. . . . . 6
MndHom
MndHom |
37 | 34, 36 | oveq12d 6668 |
. . . . 5
MndHom
MndHom |
38 | 26, 32, 37 | 3eqtr4d 2666 |
. . . 4
MndHom
MndHom |
39 | 38 | ralrimivva 2971 |
. . 3
MndHom MndHom
|
40 | 8 | adantl 482 |
. . . . 5
MndHom MndHom
|
41 | | eqid 2622 |
. . . . . . 7
|
42 | 7, 41 | mndidcl 17308 |
. . . . . 6
|
43 | 27, 42 | syl 17 |
. . . . 5
MndHom MndHom
|
44 | | fvco3 6275 |
. . . . 5
|
45 | 40, 43, 44 | syl2anc 693 |
. . . 4
MndHom MndHom
|
46 | | eqid 2622 |
. . . . . . 7
|
47 | 41, 46 | mhm0 17343 |
. . . . . 6
MndHom
|
48 | 47 | adantl 482 |
. . . . 5
MndHom MndHom
|
49 | 48 | fveq2d 6195 |
. . . 4
MndHom MndHom
|
50 | | eqid 2622 |
. . . . . 6
|
51 | 46, 50 | mhm0 17343 |
. . . . 5
MndHom
|
52 | 51 | adantr 481 |
. . . 4
MndHom MndHom
|
53 | 45, 49, 52 | 3eqtrd 2660 |
. . 3
MndHom MndHom
|
54 | 10, 39, 53 | 3jca 1242 |
. 2
MndHom MndHom
|
55 | 7, 5, 11, 23, 41, 50 | ismhm 17337 |
. 2
MndHom
|
56 | 3, 54, 55 | sylanbrc 698 |
1
MndHom MndHom
MndHom |