Description: Preimages of disjoint sets are disjoint. (Contributed by Zhi Wang, 9-Sep-2024)
Ref | Expression | ||
---|---|---|---|
Hypotheses | predisj.1 | |
|
predisj.2 | |
||
predisj.3 | |
||
predisj.4 | |
||
Assertion | predisj | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | predisj.1 | |
|
2 | predisj.2 | |
|
3 | predisj.3 | |
|
4 | predisj.4 | |
|
5 | inpreima | |
|
6 | 1 5 | syl | |
7 | 2 | imaeq2d | |
8 | ima0 | |
|
9 | 7 8 | eqtrdi | |
10 | 6 9 | eqtr3d | |
11 | 3 10 | ssdisjd | |
12 | 4 11 | ssdisjdr | |