Description: Lemma for the left side of the refrelcoss3 reflexivity theorem. (Contributed by Peter Mazsa, 1-Apr-2019)
Ref | Expression | ||
---|---|---|---|
Assertion | refrelcosslem | |- A. x e. dom ,~ R x ,~ R x |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralel | |- A. x e. dom ,~ R x e. dom ,~ R |
|
2 | eldmcoss2 | |- ( x e. _V -> ( x e. dom ,~ R <-> x ,~ R x ) ) |
|
3 | 2 | elv | |- ( x e. dom ,~ R <-> x ,~ R x ) |
4 | 3 | ralbii | |- ( A. x e. dom ,~ R x e. dom ,~ R <-> A. x e. dom ,~ R x ,~ R x ) |
5 | 1 4 | mpbi | |- A. x e. dom ,~ R x ,~ R x |