Theorem lnfnfi

Description: A linear Hilbert space functional is a functional. (Contributed by NM, 11-Feb-2006) (New usage is discouraged.)

	Ref	Expression
Hypothesis	lnfnl.1	$$⊢T\in \mathrm{LinFn}$$
Assertion	lnfnfi	$$⊢T:\mathscr{H}⟶ℂ$$

Proof

Step	Hyp	Ref	Expression
1		lnfnl.1	$$⊢T\in \mathrm{LinFn}$$
2		lnfnf	$$⊢T\in \mathrm{LinFn}\to T:\mathscr{H}⟶ℂ$$
3	1 2	ax-mp	$$⊢T:\mathscr{H}⟶ℂ$$