Metamath Proof Explorer

Theorem chub2

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

Ref Expression
Assertion chub2 
|- ( ( A e. CH /\ B e. CH ) -> A C_ ( B vH A ) )

Proof

Step Hyp Ref Expression
1 chub1 
 |-  ( ( A e. CH /\ B e. CH ) -> A C_ ( A vH B ) )
2 chjcom 
 |-  ( ( A e. CH /\ B e. CH ) -> ( A vH B ) = ( B vH A ) )
3 1 2 sseqtrd 
 |-  ( ( A e. CH /\ B e. CH ) -> A C_ ( B vH A ) )