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Theorem hvaddid2i 28801
Description: Addition with the zero vector. (Contributed by NM, 18-Aug-1999.) (New usage is discouraged.)
Hypothesis
Ref Expression
hvaddid2.1 𝐴 ∈ ℋ
Assertion
Ref Expression
hvaddid2i (0 + 𝐴) = 𝐴

Proof of Theorem hvaddid2i
StepHypRef Expression
1 hvaddid2.1 . 2 𝐴 ∈ ℋ
2 hvaddid2 28795 . 2 (𝐴 ∈ ℋ → (0 + 𝐴) = 𝐴)
31, 2ax-mp 5 1 (0 + 𝐴) = 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1538  wcel 2115  (class class class)co 7138  chba 28691   + cva 28692  0c0v 28696
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-9 2125  ax-ext 2796  ax-hvcom 28773  ax-hv0cl 28775  ax-hvaddid 28776
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-cleq 2817
This theorem is referenced by:  hvsubeq0i  28835  hvaddcani  28837  hsn0elch  29020  hhssnv  29036  shscli  29089
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