Metamath Proof Explorer


Theorem cmj2i

Description: A Hilbert lattice element commutes with its join. (Contributed by NM, 7-Aug-2004) (New usage is discouraged.)

Ref Expression
Hypotheses pjoml2.1 A C
pjoml2.2 B C
Assertion cmj2i B 𝐶 A B

Proof

Step Hyp Ref Expression
1 pjoml2.1 A C
2 pjoml2.2 B C
3 1 2 chjcli A B C
4 2 1 chub2i B A B
5 2 3 4 lecmii B 𝐶 A B