Theorem hvaddlidi 31057

Description: Addition with the zero vector. (Contributed by NM, 18-Aug-1999.) (New usage is discouraged.)

Hypothesis

Ref	Expression
hvaddlid.1	⊢ 𝐴 ∈ ℋ

Assertion

Ref	Expression
hvaddlidi	⊢ (0ℎ +ℎ 𝐴) = 𝐴

Proof of Theorem hvaddlidi

Step	Hyp	Ref	Expression
1		hvaddlid.1	. 2 ⊢ 𝐴 ∈ ℋ
2		hvaddlid 31051	. 2 ⊢ (𝐴 ∈ ℋ → (0ℎ +ℎ 𝐴) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (0ℎ +ℎ 𝐴) = 𝐴

Syntax hints:   = wceq 1536   ∈ wcel 2105  (class class class)co 7430   ℋchba 30947   +_ℎ cva 30948  0_ℎc0v 30952

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-9 2115  ax-ext 2705  ax-hvcom 31029  ax-hv0cl 31031  ax-hvaddid 31032

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1776  df-cleq 2726

This theorem is referenced by:  hvsubeq0i  31091  hvaddcani  31093  hsn0elch  31276  hhssnv  31292  shscli  31345