Description: A relation can be expressed as the set of ordered pairs in it. An analogue of dffn5 for relations. (Contributed by Mario Carneiro, 16-Aug-2015) (Revised by Thierry Arnoux, 11-May-2017)
Ref | Expression | ||
---|---|---|---|
Hypotheses | dfrel4.1 | |
|
dfrel4.2 | |
||
Assertion | dfrel4 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfrel4.1 | |
|
2 | dfrel4.2 | |
|
3 | dfrel4v | |
|
4 | nfcv | |
|
5 | nfcv | |
|
6 | 4 1 5 | nfbr | |
7 | nfcv | |
|
8 | nfcv | |
|
9 | 7 2 8 | nfbr | |
10 | nfv | |
|
11 | nfv | |
|
12 | breq12 | |
|
13 | 6 9 10 11 12 | cbvopab | |
14 | 13 | eqeq2i | |
15 | 3 14 | bitri | |