Description: Binary relation expressing the commutes relation. Definition of commutes in Kalmbach p. 20. (Contributed by NM, 6-Aug-2004) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | pjoml2.1 | |- A e. CH |
|
| pjoml2.2 | |- B e. CH |
||
| Assertion | cmbri | |- ( A C_H B <-> A = ( ( A i^i B ) vH ( A i^i ( _|_ ` B ) ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | pjoml2.1 | |- A e. CH |
|
| 2 | pjoml2.2 | |- B e. CH |
|
| 3 | cmbr | |- ( ( A e. CH /\ B e. CH ) -> ( A C_H B <-> A = ( ( A i^i B ) vH ( A i^i ( _|_ ` B ) ) ) ) ) |
|
| 4 | 1 2 3 | mp2an | |- ( A C_H B <-> A = ( ( A i^i B ) vH ( A i^i ( _|_ ` B ) ) ) ) |