Description: The left group action of element A of group G maps the underlying set X of G one-to-one onto itself. (Contributed by Paul Chapman, 18-Mar-2008) (Proof shortened by Mario Carneiro, 14-Aug-2015)
Ref | Expression | ||
---|---|---|---|
Hypotheses | grplact.1 | ||
grplact.2 | |||
grplact.3 | |||
Assertion | grplactf1o |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | grplact.1 | ||
2 | grplact.2 | ||
3 | grplact.3 | ||
4 | eqid | ||
5 | 1 2 3 4 | grplactcnv | |
6 | 5 | simpld |