Theorem chjidmi

Description: Idempotent law for Hilbert lattice join. (Contributed by NM, 15-Jun-2004) (New usage is discouraged.)

	Ref	Expression
Hypothesis	chjidm.1	$$⊢A\in {\mathbf{C}}_{\mathscr{H}}$$
Assertion	chjidmi	$$⊢A{\vee }_{\mathscr{H}}A=A$$

Proof

Step	Hyp	Ref	Expression
1		chjidm.1	$$⊢A\in {\mathbf{C}}_{\mathscr{H}}$$
2		chjidm	$$⊢A\in {\mathbf{C}}_{\mathscr{H}}\to A{\vee }_{\mathscr{H}}A=A$$
3	1 2	ax-mp	$$⊢A{\vee }_{\mathscr{H}}A=A$$