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Theorem hvaddid2i 27774
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 27768 . 2 (𝐴 ∈ ℋ → (0 + 𝐴) = 𝐴)
31, 2ax-mp 5 1 (0 + 𝐴) = 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1480  wcel 1987  (class class class)co 6615  chil 27664   + cva 27665  0c0v 27669
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-ext 2601  ax-hvcom 27746  ax-hv0cl 27748  ax-hvaddid 27749
This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1702  df-cleq 2614
This theorem is referenced by:  hvsubeq0i  27808  hvaddcani  27810  hsn0elch  27993  hhssnv  28009  shscli  28064
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