Theorem hicli

Description: Closure inference for inner product. (Contributed by NM, 1-Aug-1999) (New usage is discouraged.)

	Ref	Expression
Hypotheses	hicl.1	$$⊢A\in \mathscr{H}$$
	hicl.2	$$⊢B\in \mathscr{H}$$
Assertion	hicli	$$⊢A{\cdot }_{\mathrm{ih}}B\in ℂ$$

Proof

Step	Hyp	Ref	Expression
1		hicl.1	$$⊢A\in \mathscr{H}$$
2		hicl.2	$$⊢B\in \mathscr{H}$$
3		hicl	$$⊢\left(A\in \mathscr{H}\wedge B\in \mathscr{H}\right)\to A{\cdot }_{\mathrm{ih}}B\in ℂ$$
4	1 2 3	mp2an	$$⊢A{\cdot }_{\mathrm{ih}}B\in ℂ$$