Axiom ax-hvmulid 28203

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		chil 28116	. . 3 class ℋ
3	1, 2	wcel 2145	. 2 wff 𝐴 ∈ ℋ
4		c1 10139	. . . 4 class 1
5		csm 28118	. . . 4 class ·ℎ
6	4, 1, 5	co 6793	. . 3 class (1 ·ℎ 𝐴)
7	6, 1	wceq 1631	. 2 wff (1 ·ℎ 𝐴) = 𝐴
8	3, 7	wi 4	1 wff (𝐴 ∈ ℋ → (1 ·ℎ 𝐴) = 𝐴)

This axiom is referenced by:  hvmul0or  28222  hvsubid  28223  hvaddsubval  28230  hv2times  28258  hvnegdii  28259  hilvc  28359  hhssnv  28461  h1de2bi  28753  h1datomi  28780  mayete3i  28927  homulid2  28999  lnop0  29165  lnopaddi  29170  lnophmlem2  29216  lnfn0i  29241  lnfnaddi  29242  strlem1  29449