Description: The successor of a transitive class is transitive. (Contributed by Alan Sare, 11-Apr-2009) (Proof shortened by JJ, 24-Sep-2021)
Ref | Expression | ||
---|---|---|---|
Assertion | suctr | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elsuci | |
|
2 | trel | |
|
3 | 2 | expdimp | |
4 | eleq2 | |
|
5 | 4 | biimpcd | |
6 | 5 | adantl | |
7 | 3 6 | jaod | |
8 | 1 7 | syl5 | |
9 | 8 | expimpd | |
10 | elelsuc | |
|
11 | 9 10 | syl6 | |
12 | 11 | alrimivv | |
13 | dftr2 | |
|
14 | 12 13 | sylibr | |