Description: Two functions are equal iff their equalizer is the whole domain. (Contributed by Stefan O'Rear, 7-Mar-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | fneqeql | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqfnfv | |
|
2 | eqcom | |
|
3 | rabid2 | |
|
4 | 2 3 | bitri | |
5 | 1 4 | bitr4di | |
6 | fndmin | |
|
7 | 6 | eqeq1d | |
8 | 5 7 | bitr4d | |