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Mirrors > Home > ILE Home > Th. List > f1ocnv | Unicode version |
Description: The converse of a one-to-one onto function is also one-to-one onto. (Contributed by NM, 11-Feb-1997.) (Proof shortened by Andrew Salmon, 22-Oct-2011.) |
Ref | Expression |
---|---|
f1ocnv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fnrel 5294 | . . . . 5 | |
2 | dfrel2 5059 | . . . . . 6 | |
3 | fneq1 5284 | . . . . . . 7 | |
4 | 3 | biimprd 157 | . . . . . 6 |
5 | 2, 4 | sylbi 120 | . . . . 5 |
6 | 1, 5 | mpcom 36 | . . . 4 |
7 | 6 | anim2i 340 | . . 3 |
8 | 7 | ancoms 266 | . 2 |
9 | dff1o4 5448 | . 2 | |
10 | dff1o4 5448 | . 2 | |
11 | 8, 9, 10 | 3imtr4i 200 | 1 |
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