Theorem hvaddlidi 31322

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 31316	. 2 ⊢ (𝐴 ∈ ℋ → (0ℎ +ℎ 𝐴) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (0ℎ +ℎ 𝐴) = 𝐴

Syntax hints:   = wceq 1567   ∈ wcel 2149  (class class class)co 7411   ℋchba 31212   +_ℎ cva 31213  0_ℎc0v 31217

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-9 2159  ax-ext 2741  ax-hvcom 31294  ax-hv0cl 31296  ax-hvaddid 31297

This theorem depends on definitions:  df-bi 210  df-an 401  df-ex 1807  df-cleq 2761

This theorem is referenced by:  hvsubeq0i  31356  hvaddcani  31358  hsn0elch  31541  hhssnv  31557  shscli  31610