Theorem chdmj1i

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	chdmj1i	|- ( _|_ ` ( 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 2	chdmm4i	|- ( _|_ ` ( ( _|_ ` A ) i^i ( _|_ ` B ) ) ) = ( A vH B )
4	3	fveq2i	|- ( _|_ ` ( _|_ ` ( ( _|_ ` A ) i^i ( _|_ ` B ) ) ) ) = ( _|_ ` ( A vH B ) )
5	1	choccli	|- ( _|_ ` A ) e. CH
6	2	choccli	|- ( _|_ ` B ) e. CH
7	5 6	chincli	|- ( ( _|_ ` A ) i^i ( _|_ ` B ) ) e. CH
8	7	pjococi	|- ( _|_ ` ( _|_ ` ( ( _|_ ` A ) i^i ( _|_ ` B ) ) ) ) = ( ( _|_ ` A ) i^i ( _|_ ` B ) )
9	4 8	eqtr3i	|- ( _|_ ` ( A vH B ) ) = ( ( _|_ ` A ) i^i ( _|_ ` B ) )