Axiom ax-hvmulid 22509

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

Assertion

Ref	Expression
ax-hvmulid	|- ( A e. ~H -> ( 1 .h A ) = A )

Detailed syntax breakdown of Axiom ax-hvmulid

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2		chil 22422	. . 3 class ~H
3	1, 2	wcel 1725	. 2 wff A e. ~H
4		c1 8991	. . . 4 class 1
5		csm 22424	. . . 4 class .h
6	4, 1, 5	co 6081	. . 3 class ( 1 .h A )
7	6, 1	wceq 1652	. 2 wff ( 1 .h A ) = A
8	3, 7	wi 4	1 wff ( A e. ~H -> ( 1 .h A ) = A )

This axiom is referenced by:  hvmul0or  22527  hvsubid  22528  hvaddsubval  22535  hv2times  22563  hvnegdii  22564  hilvc  22664  hhssnv  22764  h1de2bi  23056  h1datomi  23083  mayete3i  23230  mayete3iOLD  23231  homulid2  23303  lnop0  23469  lnopaddi  23474  lnophmlem2  23520  lnfn0i  23545  lnfnaddi  23546  strlem1  23753