Theorem hvcom 8884

Description: Commutation of vector addition.

Hypotheses

Ref	Expression
hvaddcl.1	|- A e. H~
hvaddcl.2	|- B e. H~

Assertion

Ref	Expression
hvcom	|- (A +h B) = (B +h A)

Proof of Theorem hvcom

Step	Hyp	Ref	Expression
1		hvaddcl.1	. 2 |- A e. H~
2		hvaddcl.2	. 2 |- B e. H~
3		ax-hvcom 8866	. 2 |- ((A e. H~ /\ B e. H~) -> (A +h B) = (B +h A))
4	1, 2, 3	mp2an 699	1 |- (A +h B) = (B +h A)

Syntax hints:   = wceq 958   e. wcel 960  (class class class)co 3969  H~chil 8783   +h cva 8784

This theorem is referenced by:  hvsub23 8918  hvadd12 8919  hvnegdi 8924  norm3dif 9009  normpar2 9018  nonbool 9591  lnophmlem2 9937

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-hvcom 8866

This theorem depends on definitions:  df-bi 147  df-an 225

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