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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 e. CH
pjoml2.2 
|- B e. CH
Assertion cmj2i 
|- B C_H ( A vH B )

Proof

Step Hyp Ref Expression
1 pjoml2.1 
 |-  A e. CH
2 pjoml2.2 
 |-  B e. CH
3 1 2 chjcli 
 |-  ( A vH B ) e. CH
4 2 1 chub2i 
 |-  B C_ ( A vH B )
5 2 3 4 lecmii 
 |-  B C_H ( A vH B )