Description: The rank of the union of two sets. Theorem 15.17(iii) of Monk1 p. 112. (Contributed by NM, 26-Nov-2003) (Revised by Mario Carneiro, 17-Nov-2014)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ranksn.1 | |
|
rankun.2 | |
||
Assertion | rankun | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ranksn.1 | |
|
2 | rankun.2 | |
|
3 | unir1 | |
|
4 | 1 3 | eleqtrri | |
5 | 2 3 | eleqtrri | |
6 | rankunb | |
|
7 | 4 5 6 | mp2an | |