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Theorem hvcomi 22512
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
StepHypRef Expression
1 hvaddcl.1 . 2  |-  A  e. 
~H
2 hvaddcl.2 . 2  |-  B  e. 
~H
3 ax-hvcom 22494 . 2  |-  ( ( A  e.  ~H  /\  B  e.  ~H )  ->  ( A  +h  B
)  =  ( B  +h  A ) )
41, 2, 3mp2an 654 1  |-  ( A  +h  B )  =  ( B  +h  A
)
Colors of variables: wff set class
Syntax hints:    = wceq 1652    e. wcel 1725  (class class class)co 6073   ~Hchil 22412    +h cva 22413
This theorem is referenced by:  hvadd12i  22549  hvnegdii  22554  norm3difi  22639  normpar2i  22648  nonbooli  23143  lnophmlem2  23510
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-hvcom 22494
This theorem depends on definitions:  df-bi 178  df-an 361
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