Theorem hvaddid2i 27270

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	⊢ (0ℎ +ℎ 𝐴) = 𝐴

Proof of Theorem hvaddid2i

Step	Hyp	Ref	Expression
1		hvaddid2.1	. 2 ⊢ 𝐴 ∈ ℋ
2		hvaddid2 27264	. 2 ⊢ (𝐴 ∈ ℋ → (0ℎ +ℎ 𝐴) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (0ℎ +ℎ 𝐴) = 𝐴

Syntax hints:   = wceq 1475   ∈ wcel 1977  (class class class)co 6549   ℋchil 27160   +_ℎ cva 27161  0_ℎc0v 27165

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-ext 2590  ax-hvcom 27242  ax-hv0cl 27244  ax-hvaddid 27245

This theorem depends on definitions:  df-bi 196  df-an 385  df-cleq 2603

This theorem is referenced by:  hvsubeq0i  27304  hvaddcani  27306  hsn0elch  27489  hhssnv  27505  shscli  27560