Metamath Proof Explorer


Theorem chjcomi

Description: Commutative law for join in CH . (Contributed by NM, 14-Oct-1999) (New usage is discouraged.)

Ref Expression
Hypotheses ch0le.1
|- A e. CH
chjcl.2
|- B e. CH
Assertion chjcomi
|- ( A vH B ) = ( B vH A )

Proof

Step Hyp Ref Expression
1 ch0le.1
 |-  A e. CH
2 chjcl.2
 |-  B e. CH
3 1 chshii
 |-  A e. SH
4 2 chshii
 |-  B e. SH
5 3 4 shjcomi
 |-  ( A vH B ) = ( B vH A )