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 A C
chjcl.2 B C
chlub.1 C C
Assertion chlubi A C B C A B C


Step Hyp Ref Expression
1 ch0le.1 A C
2 chjcl.2 B C
3 chlub.1 C C
4 1 chshii A S
5 2 chshii B S
6 4 5 3 shlubi A C B C A B C