Metamath Proof Explorer

Theorem chjcl

Description: Closure of join in CH . (Contributed by NM, 2-Nov-1999) (New usage is discouraged.)

Ref Expression
Assertion chjcl 
|- ( ( A e. CH /\ B e. CH ) -> ( A vH B ) e. CH )

Proof

Step Hyp Ref Expression
1 chsh 
 |-  ( A e. CH -> A e. SH )
2 chsh 
 |-  ( B e. CH -> B e. SH )
3 shjcl 
 |-  ( ( A e. SH /\ B e. SH ) -> ( A vH B ) e. CH )
4 1 2 3 syl2an 
 |-  ( ( A e. CH /\ B e. CH ) -> ( A vH B ) e. CH )