Metamath Proof Explorer

Theorem chub1

Description: Hilbert lattice join is greater than or equal to its first argument. (Contributed by NM, 12-Jun-2004) (New usage is discouraged.)

Ref Expression
Assertion chub1 
|- ( ( A e. CH /\ B e. CH ) -> A C_ ( A vH B ) )

Proof

Step Hyp Ref Expression
1 chsh 
 |-  ( A e. CH -> A e. SH )
2 chsh 
 |-  ( B e. CH -> B e. SH )
3 shub1 
 |-  ( ( A e. SH /\ B e. SH ) -> A C_ ( A vH B ) )
4 1 2 3 syl2an 
 |-  ( ( A e. CH /\ B e. CH ) -> A C_ ( A vH B ) )