Description: The range of the R1 function is transitive. Lemma 2.10 of Kunen p. 97. (Contributed by Mario Carneiro, 22-Mar-2013) (Revised by Mario Carneiro, 16-Nov-2014)
Ref | Expression | ||
---|---|---|---|
Hypothesis | r1elss.1 | |
|
Assertion | r1elss | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | r1elss.1 | |
|
2 | r1elssi | |
|
3 | 1 | tz9.12 | |
4 | dfss3 | |
|
5 | r1fnon | |
|
6 | fnfun | |
|
7 | funiunfv | |
|
8 | 5 6 7 | mp2b | |
9 | 8 | eleq2i | |
10 | eliun | |
|
11 | 9 10 | bitr3i | |
12 | 11 | ralbii | |
13 | 4 12 | bitri | |
14 | 8 | eleq2i | |
15 | eliun | |
|
16 | 14 15 | bitr3i | |
17 | 3 13 16 | 3imtr4i | |
18 | 2 17 | impbii | |