Theorem chj12i

Description: A rearrangement of Hilbert lattice join. (Contributed by NM, 29-Apr-2006) (New usage is discouraged.)

	Ref	Expression
Hypotheses	chj12.1	|- A e. CH
	chj12.2	|- B e. CH
	chj12.3	|- C e. CH
Assertion	chj12i	|- ( A vH ( B vH C ) ) = ( B vH ( A vH C ) )

Proof

Step	Hyp	Ref	Expression
1		chj12.1	|- A e. CH
2		chj12.2	|- B e. CH
3		chj12.3	|- C e. CH
4	1 2	chjcomi	|- ( A vH B ) = ( B vH A )
5	4	oveq1i	|- ( ( A vH B ) vH C ) = ( ( B vH A ) vH C )
6	1 2 3	chjassi	|- ( ( A vH B ) vH C ) = ( A vH ( B vH C ) )
7	2 1 3	chjassi	|- ( ( B vH A ) vH C ) = ( B vH ( A vH C ) )
8	5 6 7	3eqtr3i	|- ( A vH ( B vH C ) ) = ( B vH ( A vH C ) )