Metamath Proof Explorer

Theorem chjcli

Description: Closure of CH join. (Contributed by NM, 29-Jul-1999) (New usage is discouraged.)

Ref Expression
Hypotheses ch0le.1 
|- A e. CH
chjcl.2 
|- B e. CH
Assertion chjcli 
|- ( A vH B ) e. CH

Proof

Step Hyp Ref Expression
1 ch0le.1 
 |-  A e. CH
2 chjcl.2 
 |-  B e. CH
3 1 chshii 
 |-  A e. SH
4 2 chshii 
 |-  B e. SH
5 3 4 shjcli 
 |-  ( A vH B ) e. CH