Description: The membership relation for a relation is inherited by class union. (Contributed by NM, 17-Sep-2006)
Ref | Expression | ||
---|---|---|---|
Assertion | unielrel | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elrel | |
|
2 | simpr | |
|
3 | vex | |
|
4 | vex | |
|
5 | 3 4 | uniopel | |
6 | 5 | a1i | |
7 | eleq1 | |
|
8 | unieq | |
|
9 | 8 | eleq1d | |
10 | 6 7 9 | 3imtr4d | |
11 | 10 | exlimivv | |
12 | 1 2 11 | sylc | |