Axiom ax-hvass 9147

Description: Vector addition is associative.

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 9063	. . . 4 class H~
3	1, 2	wcel 994	. . 3 wff A e. H~
4		cB	. . . 4 class B
5	4, 2	wcel 994	. . 3 wff B e. H~
6		cC	. . . 4 class C
7	6, 2	wcel 994	. . 3 wff C e. H~
8	3, 5, 7	w3a 781	. 2 wff (A e. H~ /\ B e. H~ /\ C e. H~)
9		cva 9064	. . . . 5 class +h
10	1, 4, 9	co 4021	. . . 4 class (A +h B)
11	10, 6, 9	co 4021	. . 3 class ((A +h B) +h C)
12	4, 6, 9	co 4021	. . . 4 class (B +h C)
13	1, 12, 9	co 4021	. . 3 class (A +h (B +h C))
14	11, 13	wceq 992	. 2 wff ((A +h B) +h C) = (A +h (B +h C))
15	8, 14	wi 3	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:  hvadd23 9178  hvadd12 9179  hvadd4 9180  hvpncan 9183  hvaddsubass 9185  hvassi 9195  hilabl 9303  spanunsni 9778  hoaddassi 9982

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