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Theorem hvcomi 30537
Description: Commutation of vector addition. (Contributed by NM, 3-Sep-1999.) (New usage is discouraged.)
Hypotheses
Ref Expression
hvaddcl.1 𝐴 ∈ ℋ
hvaddcl.2 𝐵 ∈ ℋ
Assertion
Ref Expression
hvcomi (𝐴 + 𝐵) = (𝐵 + 𝐴)

Proof of Theorem hvcomi
StepHypRef Expression
1 hvaddcl.1 . 2 𝐴 ∈ ℋ
2 hvaddcl.2 . 2 𝐵 ∈ ℋ
3 ax-hvcom 30519 . 2 ((𝐴 ∈ ℋ ∧ 𝐵 ∈ ℋ) → (𝐴 + 𝐵) = (𝐵 + 𝐴))
41, 2, 3mp2an 688 1 (𝐴 + 𝐵) = (𝐵 + 𝐴)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1539  wcel 2104  (class class class)co 7413  chba 30437   + cva 30438
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-hvcom 30519
This theorem depends on definitions:  df-bi 206  df-an 395
This theorem is referenced by:  hvadd12i  30575  hvnegdii  30580  norm3difi  30665  normpar2i  30674  nonbooli  31169  lnophmlem2  31535
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