Metamath Proof Explorer

Theorem cmm2i

Description: A Hilbert lattice element commutes with its meet. (Contributed by NM, 7-Aug-2004) (New usage is discouraged.)

Ref Expression
Hypotheses pjoml2.1 
|- A e. CH
pjoml2.2 
|- B e. CH
Assertion cmm2i 
|- B C_H ( A i^i B )

Proof

Step Hyp Ref Expression
1 pjoml2.1 
 |-  A e. CH
2 pjoml2.2 
 |-  B e. CH
3 2 1 cmm1i 
 |-  B C_H ( B i^i A )
4 incom 
 |-  ( B i^i A ) = ( A i^i B )
5 3 4 breqtri 
 |-  B C_H ( A i^i B )