Description: Commutation is symmetric. Theorem 2(v) of Kalmbach p. 22. (Contributed by NM, 4-Nov-2000) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | pjoml2.1 | |- A e. CH |
|
pjoml2.2 | |- B e. CH |
||
Assertion | cmcmi | |- ( A C_H B <-> B C_H A ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pjoml2.1 | |- A e. CH |
|
2 | pjoml2.2 | |- B e. CH |
|
3 | 1 2 | cmcmlem | |- ( A C_H B -> B C_H A ) |
4 | 2 1 | cmcmlem | |- ( B C_H A -> A C_H B ) |
5 | 3 4 | impbii | |- ( A C_H B <-> B C_H A ) |