ax-hvmulid - Hilbert Space Explorer

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Axiom ax-hvmulid 30297

Description: Scalar multiplication by one. (Contributed by NM, 30-May-1999.) (New usage is discouraged.)

**Assertion**
Ref	Expression
ax-hvmulid	⊢ (𝐴 ∈ ℋ → (1 ·_ℎ 𝐴) = 𝐴)

**Detailed syntax breakdown of Axiom ax-hvmulid**
Step	Hyp	Ref	Expression
1		cA	. . 3 class 𝐴
2		chba 30210	. . 3 class ℋ
3	1, 2	wcel 2106	. 2 wff 𝐴 ∈ ℋ
4		c1 11113	. . . 4 class 1
5		csm 30212	. . . 4 class ·_ℎ
6	4, 1, 5	co 7411	. . 3 class (1 ·_ℎ 𝐴)
7	6, 1	wceq 1541	. 2 wff (1 ·_ℎ 𝐴) = 𝐴
8	3, 7	wi 4	1 wff (𝐴 ∈ ℋ → (1 ·_ℎ 𝐴) = 𝐴)

Colors of variables: wff setvar class

This axiom is referenced by: hvmul0or 30316 hvsubid 30317 hvaddsubval 30324 hv2times 30352 hvnegdii 30353 hilvc 30453 hhssnv 30555 h1de2bi 30845 h1datomi 30872 mayete3i 31019 homullid 31091 lnop0 31257 lnopaddi 31262 lnophmlem2 31308 lnfn0i 31333 lnfnaddi 31334 strlem1 31541