Description: Build a bijection by restricting the domain of a bijection. (Contributed by AV, 31-Jul-2022)
Ref | Expression | ||
---|---|---|---|
Hypotheses | f1oresf1o.1 | |
|
f1oresf1o.2 | |
||
f1oresf1o.3 | |
||
Assertion | f1oresf1o | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1oresf1o.1 | |
|
2 | f1oresf1o.2 | |
|
3 | f1oresf1o.3 | |
|
4 | f1of1 | |
|
5 | 1 4 | syl | |
6 | f1ores | |
|
7 | 5 2 6 | syl2anc | |
8 | f1ofun | |
|
9 | 1 8 | syl | |
10 | f1odm | |
|
11 | 1 10 | syl | |
12 | 2 11 | sseqtrrd | |
13 | dfimafn | |
|
14 | 9 12 13 | syl2anc | |
15 | 3 | abbidv | |
16 | df-rab | |
|
17 | 15 16 | eqtr4di | |
18 | 14 17 | eqtr2d | |
19 | 18 | f1oeq3d | |
20 | 7 19 | mpbird | |