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Theorem hvaddid2i 28733
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 28727 . 2 (𝐴 ∈ ℋ → (0 + 𝐴) = 𝐴)
31, 2ax-mp 5 1 (0 + 𝐴) = 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1528  wcel 2105  (class class class)co 7145  chba 28623   + cva 28624  0c0v 28628
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-9 2115  ax-ext 2790  ax-hvcom 28705  ax-hv0cl 28707  ax-hvaddid 28708
This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1772  df-cleq 2811
This theorem is referenced by:  hvsubeq0i  28767  hvaddcani  28769  hsn0elch  28952  hhssnv  28968  shscli  29021
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