Theorem chdmj3i

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	chdmj3i	|- ( _|_ ` ( 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	2	choccli	|- ( _|_ ` B ) e. CH
4	1 3	chdmj1i	|- ( _|_ ` ( A vH ( _|_ ` B ) ) ) = ( ( _|_ ` A ) i^i ( _|_ ` ( _|_ ` B ) ) )
5	2	pjococi	|- ( _|_ ` ( _|_ ` B ) ) = B
6	5	ineq2i	|- ( ( _|_ ` A ) i^i ( _|_ ` ( _|_ ` B ) ) ) = ( ( _|_ ` A ) i^i B )
7	4 6	eqtri	|- ( _|_ ` ( A vH ( _|_ ` B ) ) ) = ( ( _|_ ` A ) i^i B )