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Mirrors > Home > MPE Home > Th. List > df-ghm | Structured version Unicode version |
Description: A homomorphism of groups is a map between two structures which preserves the group operation. Requiring both sides to be groups simplifies most theorems at the cost of complicating the theorem which pushes forward a group structure. (Contributed by Stefan O'Rear, 31-Dec-2014.) |
Ref | Expression |
---|---|
df-ghm |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cghm 15862 |
. 2
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2 | vs |
. . 3
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3 | vt |
. . 3
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4 | cgrp 15528 |
. . 3
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5 | vw |
. . . . . . . 8
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6 | 5 | cv 1369 |
. . . . . . 7
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7 | 3 | cv 1369 |
. . . . . . . 8
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8 | cbs 14291 |
. . . . . . . 8
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9 | 7, 8 | cfv 5525 |
. . . . . . 7
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10 | vg |
. . . . . . . 8
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11 | 10 | cv 1369 |
. . . . . . 7
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12 | 6, 9, 11 | wf 5521 |
. . . . . 6
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13 | vx |
. . . . . . . . . . . 12
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14 | 13 | cv 1369 |
. . . . . . . . . . 11
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15 | vy |
. . . . . . . . . . . 12
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16 | 15 | cv 1369 |
. . . . . . . . . . 11
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17 | 2 | cv 1369 |
. . . . . . . . . . . 12
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18 | cplusg 14356 |
. . . . . . . . . . . 12
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19 | 17, 18 | cfv 5525 |
. . . . . . . . . . 11
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20 | 14, 16, 19 | co 6199 |
. . . . . . . . . 10
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21 | 20, 11 | cfv 5525 |
. . . . . . . . 9
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22 | 14, 11 | cfv 5525 |
. . . . . . . . . 10
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23 | 16, 11 | cfv 5525 |
. . . . . . . . . 10
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24 | 7, 18 | cfv 5525 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() |
25 | 22, 23, 24 | co 6199 |
. . . . . . . . 9
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26 | 21, 25 | wceq 1370 |
. . . . . . . 8
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27 | 26, 15, 6 | wral 2798 |
. . . . . . 7
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28 | 27, 13, 6 | wral 2798 |
. . . . . 6
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29 | 12, 28 | wa 369 |
. . . . 5
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30 | 17, 8 | cfv 5525 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() |
31 | 29, 5, 30 | wsbc 3292 |
. . . 4
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32 | 31, 10 | cab 2439 |
. . 3
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33 | 2, 3, 4, 4, 32 | cmpt2 6201 |
. 2
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34 | 1, 33 | wceq 1370 |
1
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Colors of variables: wff setvar class |
This definition is referenced by: reldmghm 15864 isghm 15865 |
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