Description: An isomorphism from one well-order to another can be restricted on either well-order. (Contributed by Mario Carneiro, 15-Jan-2013)
Ref | Expression | ||
---|---|---|---|
Assertion | isores1 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isocnv | |
|
2 | isores2 | |
|
3 | 1 2 | sylib | |
4 | isocnv | |
|
5 | 3 4 | syl | |
6 | isof1o | |
|
7 | f1orel | |
|
8 | dfrel2 | |
|
9 | isoeq1 | |
|
10 | 8 9 | sylbi | |
11 | 6 7 10 | 3syl | |
12 | 5 11 | mpbid | |
13 | isocnv | |
|
14 | 13 2 | sylibr | |
15 | isocnv | |
|
16 | 14 15 | syl | |
17 | isof1o | |
|
18 | isoeq1 | |
|
19 | 8 18 | sylbi | |
20 | 17 7 19 | 3syl | |
21 | 16 20 | mpbid | |
22 | 12 21 | impbii | |