Theorem bracl

Description: Closure of the bra function. (Contributed by NM, 23-May-2006) (New usage is discouraged.)

	Ref	Expression
Assertion	bracl	$$⊢\left(A\in \mathscr{H}\wedge B\in \mathscr{H}\right)\to \mathrm{bra}\left(A\right)\left(B\right)\in ℂ$$

Proof

Step	Hyp	Ref	Expression
1		brafn	$$⊢A\in \mathscr{H}\to \mathrm{bra}\left(A\right):\mathscr{H}⟶ℂ$$
2	1	ffvelrnda	$$⊢\left(A\in \mathscr{H}\wedge B\in \mathscr{H}\right)\to \mathrm{bra}\left(A\right)\left(B\right)\in ℂ$$