Description: A transitive Tarski class is closed under small unions. (Contributed by Mario Carneiro, 22-Jun-2013)
Ref | Expression | ||
---|---|---|---|
Assertion | tskurn | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp1l | |
|
2 | simp1r | |
|
3 | frn | |
|
4 | 3 | 3ad2ant3 | |
5 | tskwe2 | |
|
6 | 1 5 | syl | |
7 | simp2 | |
|
8 | trss | |
|
9 | 2 7 8 | sylc | |
10 | ssnum | |
|
11 | 6 9 10 | syl2anc | |
12 | ffn | |
|
13 | dffn4 | |
|
14 | 12 13 | sylib | |
15 | 14 | 3ad2ant3 | |
16 | fodomnum | |
|
17 | 11 15 16 | sylc | |
18 | tsksdom | |
|
19 | 1 7 18 | syl2anc | |
20 | domsdomtr | |
|
21 | 17 19 20 | syl2anc | |
22 | tskssel | |
|
23 | 1 4 21 22 | syl3anc | |
24 | tskuni | |
|
25 | 1 2 23 24 | syl3anc | |