Description: Restricting a relation to its domain without a set is the same as restricting the relation to the universe without this set. (Contributed by AV, 2-Dec-2018)
Ref | Expression | ||
---|---|---|---|
Assertion | resdmdfsn | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | resindm | |
|
2 | indif1 | |
|
3 | incom | |
|
4 | inv1 | |
|
5 | 3 4 | eqtri | |
6 | 5 | difeq1i | |
7 | 2 6 | eqtri | |
8 | 7 | reseq2i | |
9 | 1 8 | eqtr3di | |