Description: The inverse function of a group. (Contributed by NM, 26-Oct-2006) (Revised by Mario Carneiro, 15-Dec-2013) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | grpinvfval.1 | |
|
grpinvfval.2 | |
||
grpinvfval.3 | |
||
Assertion | grpoinvfval | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | grpinvfval.1 | |
|
2 | grpinvfval.2 | |
|
3 | grpinvfval.3 | |
|
4 | rnexg | |
|
5 | 1 4 | eqeltrid | |
6 | mptexg | |
|
7 | 5 6 | syl | |
8 | rneq | |
|
9 | 8 1 | eqtr4di | |
10 | oveq | |
|
11 | fveq2 | |
|
12 | 11 2 | eqtr4di | |
13 | 10 12 | eqeq12d | |
14 | 9 13 | riotaeqbidv | |
15 | 9 14 | mpteq12dv | |
16 | df-ginv | |
|
17 | 15 16 | fvmptg | |
18 | 7 17 | mpdan | |
19 | 3 18 | eqtrid | |