Metamath Proof Explorer

Theorem chlej1i

Description: Add join to both sides of a Hilbert lattice ordering. (Contributed by NM, 19-Oct-1999) (New usage is discouraged.)

Ref Expression
Hypotheses ch0le.1 A C
chjcl.2 B C
chlub.1 C C
Assertion chlej1i A B A C 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 3 chshii C S
7 4 5 6 shlej1i A B A C B C