Axiom ax-hvmulid 28474

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 28387	. . 3 class ℋ
3	1, 2	wcel 2081	. 2 wff 𝐴 ∈ ℋ
4		c1 10384	. . . 4 class 1
5		csm 28389	. . . 4 class ·ℎ
6	4, 1, 5	co 7016	. . 3 class (1 ·ℎ 𝐴)
7	6, 1	wceq 1522	. 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  28493  hvsubid  28494  hvaddsubval  28501  hv2times  28529  hvnegdii  28530  hilvc  28630  hhssnv  28732  h1de2bi  29022  h1datomi  29049  mayete3i  29196  homulid2  29268  lnop0  29434  lnopaddi  29439  lnophmlem2  29485  lnfn0i  29510  lnfnaddi  29511  strlem1  29718