Metamath Proof Explorer

Theorem shjcli

Description: Closure of CH join. (Contributed by NM, 19-Oct-1999) (New usage is discouraged.)

Ref Expression
Hypotheses shincl.1 
|- A e. SH
shincl.2 
|- B e. SH
Assertion shjcli 
|- ( A vH B ) e. CH

Proof

Step Hyp Ref Expression
1 shincl.1 
 |-  A e. SH
2 shincl.2 
 |-  B e. SH
3 shjcl 
 |-  ( ( A e. SH /\ B e. SH ) -> ( A vH B ) e. CH )
4 1 2 3 mp2an 
 |-  ( A vH B ) e. CH