Metamath Proof Explorer


Theorem chlubi

Description: Hilbert lattice join is the least upper bound of two elements. (Contributed by NM, 11-Jun-2004) (New usage is discouraged.)

Ref Expression
Hypotheses ch0le.1 AC
chjcl.2 BC
chlub.1 CC
Assertion chlubi ACBCABC

Proof

Step Hyp Ref Expression
1 ch0le.1 AC
2 chjcl.2 BC
3 chlub.1 CC
4 1 chshii AS
5 2 chshii BS
6 4 5 3 shlubi ACBCABC