Theorem hvcom 8889

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 8871	. 2 |- ((A e. H~ /\ B e. H~) -> (A +h B) = (B +h A))
4	1, 2, 3	mp2an 697	1 |- (A +h B) = (B +h A)

Syntax hints:   = wceq 956   e. wcel 958  (class class class)co 3963  H~chil 8788   +h cva 8789

This theorem is referenced by:  hvsub23 8923  hvadd12 8924  hvnegdi 8929  norm3dif 9014  normpar2 9023  nonbool 9596  lnophmlem2 9942

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-hvcom 8871

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

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