Theorem chdmj2i

Description: De Morgan's law for join in a Hilbert lattice. (Contributed by NM, 21-Jun-2004) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ch0le.1	|- A e. CH
	chjcl.2	|- B e. CH
Assertion	chdmj2i	|- ( _|_ ` ( ( _|_ ` A ) vH B ) ) = ( A i^i ( _|_ ` B ) )

Proof

Step	Hyp	Ref	Expression
1		ch0le.1	|- A e. CH
2		chjcl.2	|- B e. CH
3	1	choccli	|- ( _|_ ` A ) e. CH
4	3 2	chdmj1i	|- ( _|_ ` ( ( _|_ ` A ) vH B ) ) = ( ( _|_ ` ( _|_ ` A ) ) i^i ( _|_ ` B ) )
5	1	pjococi	|- ( _|_ ` ( _|_ ` A ) ) = A
6	5	ineq1i	|- ( ( _|_ ` ( _|_ ` A ) ) i^i ( _|_ ` B ) ) = ( A i^i ( _|_ ` B ) )
7	4 6	eqtri	|- ( _|_ ` ( ( _|_ ` A ) vH B ) ) = ( A i^i ( _|_ ` B ) )