Description: Construct an explicit bijection from A .o B to B .o A . (Contributed by Mario Carneiro, 30-May-2015)
Ref | Expression | ||
---|---|---|---|
Hypotheses | omf1o.1 | |
|
omf1o.2 | |
||
Assertion | omf1o | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | omf1o.1 | |
|
2 | omf1o.2 | |
|
3 | eqid | |
|
4 | 3 | omxpenlem | |
5 | 4 | ancoms | |
6 | eqid | |
|
7 | 6 | xpcomf1o | |
8 | f1oco | |
|
9 | 5 7 8 | sylancl | |
10 | 6 3 | xpcomco | |
11 | 2 10 | eqtr4i | |
12 | f1oeq1 | |
|
13 | 11 12 | ax-mp | |
14 | 9 13 | sylibr | |
15 | 1 | omxpenlem | |
16 | f1ocnv | |
|
17 | 15 16 | syl | |
18 | f1oco | |
|
19 | 14 17 18 | syl2anc | |