Description: Alternate definition of one-to-one onto function. (Contributed by NM, 10-Feb-1997) (Proof shortened by Andrew Salmon, 22-Oct-2011)
Ref | Expression | ||
---|---|---|---|
Assertion | dff1o2 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-f1o | |
|
2 | df-f1 | |
|
3 | df-fo | |
|
4 | 2 3 | anbi12i | |
5 | anass | |
|
6 | 3anan12 | |
|
7 | 6 | anbi1i | |
8 | eqimss | |
|
9 | df-f | |
|
10 | 9 | biimpri | |
11 | 8 10 | sylan2 | |
12 | 11 | 3adant2 | |
13 | 12 | pm4.71i | |
14 | ancom | |
|
15 | 7 13 14 | 3bitr4ri | |
16 | 5 15 | bitri | |
17 | 4 16 | bitri | |
18 | 1 17 | bitri | |