Axiom ax-hvass 27859

Description: Vector addition is associative. (Contributed by NM, 3-Sep-1999.) (New usage is discouraged.)

Assertion

Ref	Expression
ax-hvass	|- ( ( A e. ~H /\ B e. ~H /\ C e. ~H ) -> ( ( A +h B ) +h C ) = ( A +h ( B +h C ) ) )

Detailed syntax breakdown of Axiom ax-hvass

Step	Hyp	Ref	Expression
1		cA	. . . 4 class A
2		chil 27776	. . . 4 class ~H
3	1, 2	wcel 1990	. . 3 wff A e. ~H
4		cB	. . . 4 class B
5	4, 2	wcel 1990	. . 3 wff B e. ~H
6		cC	. . . 4 class C
7	6, 2	wcel 1990	. . 3 wff C e. ~H
8	3, 5, 7	w3a 1037	. 2 wff ( A e. ~H /\ B e. ~H /\ C e. ~H )
9		cva 27777	. . . . 5 class +h
10	1, 4, 9	co 6650	. . . 4 class ( A +h B )
11	10, 6, 9	co 6650	. . 3 class ( ( A +h B ) +h C )
12	4, 6, 9	co 6650	. . . 4 class ( B +h C )
13	1, 12, 9	co 6650	. . 3 class ( A +h ( B +h C ) )
14	11, 13	wceq 1483	. 2 wff ( ( A +h B ) +h C ) = ( A +h ( B +h C ) )
15	8, 14	wi 4	1 wff ( ( A e. ~H /\ B e. ~H /\ C e. ~H ) -> ( ( A +h B ) +h C ) = ( A +h ( B +h C ) ) )

This axiom is referenced by:  hvadd32  27891  hvadd12  27892  hvadd4  27893  hvpncan  27896  hvaddsubass  27898  hvassi  27910  hilablo  28017  spanunsni  28438  hoaddassi  28635