Metamath Proof Explorer

Theorem chjval

Description: Value of join in CH . (Contributed by NM, 9-Aug-2000) (New usage is discouraged.)

Ref Expression
Assertion chjval 
|- ( ( A e. CH /\ B e. CH ) -> ( A vH B ) = ( _|_ ` ( _|_ ` ( A u. B ) ) ) )

Proof

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