Description: Each member of an ordered pair belongs to the union of the union of a class to which the ordered pair belongs. Lemma 3D of Enderton p. 41. (Contributed by NM, 31-Mar-1995) (Revised by Mario Carneiro, 27-Feb-2016)
Ref | Expression | ||
---|---|---|---|
Hypotheses | opeluu.1 | |
|
opeluu.2 | |
||
Assertion | opeluu | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opeluu.1 | |
|
2 | opeluu.2 | |
|
3 | 1 | prid1 | |
4 | 1 2 | opi2 | |
5 | elunii | |
|
6 | 4 5 | mpan | |
7 | elunii | |
|
8 | 3 6 7 | sylancr | |
9 | 2 | prid2 | |
10 | elunii | |
|
11 | 9 6 10 | sylancr | |
12 | 8 11 | jca | |