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 ) ) ) ) |