Description: A lattice element that commutes with two others also commutes with their join. Theorem 4.2 of Beran p. 49. (Contributed by NM, 11-May-2009) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | fh1.1 | |
|
fh1.2 | |
||
fh1.3 | |
||
fh1.4 | |
||
fh1.5 | |
||
Assertion | cm2ji | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fh1.1 | |
|
2 | fh1.2 | |
|
3 | fh1.3 | |
|
4 | fh1.4 | |
|
5 | fh1.5 | |
|
6 | 1 2 3 | 3pm3.2i | |
7 | 4 5 | pm3.2i | |
8 | cm2j | |
|
9 | 6 7 8 | mp2an | |