Theorem hvcom 5000

Description: Commutation of vector addition.

Hypotheses

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

Assertion

Ref	Expression
hvcom	|- (A +v B) = (B +v 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 4985	. 2 |- ((A e. H~ /\ B e. H~) -> (A +v B) = (B +v A))
4	1, 2, 3	mp2an 520	1 |- (A +v B) = (B +v A)

Syntax hints:   = wceq 1091   e. wcel 1092  (class class class)co 3001  H~chil 4958   +v cva 4959

This theorem is referenced by:  hvsub23 5028  hvadd12 5029  hvnegdi 5034  norm3dif 5094  normpar2 5100

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-hvcom 4985

This theorem depends on definitions:  df-bi 128  df-an 198

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