Theorem hvcomi 27876

Description: Commutation of vector addition. (Contributed by NM, 3-Sep-1999.) (New usage is discouraged.)

Hypotheses

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

Assertion

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

Proof of Theorem hvcomi

Step	Hyp	Ref	Expression
1		hvaddcl.1	. 2 |- A e. ~H
2		hvaddcl.2	. 2 |- B e. ~H
3		ax-hvcom 27858	. 2 |- ( ( A e. ~H /\ B e. ~H ) -> ( A +h B ) = ( B +h A ) )
4	1, 2, 3	mp2an 708	1 |- ( A +h B ) = ( B +h A )

Syntax hints:   = wceq 1483   e. wcel 1990  (class class class)co 6650   ~Hchil 27776   +h cva 27777

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-hvcom 27858

This theorem depends on definitions:  df-bi 197  df-an 386

This theorem is referenced by:  hvadd12i  27914  hvnegdii  27919  norm3difi  28004  normpar2i  28013  nonbooli  28510  lnophmlem2  28876