Theorem hvaddlidi 30962

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 30956	. 2 ⊢ (𝐴 ∈ ℋ → (0ℎ +ℎ 𝐴) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (0ℎ +ℎ 𝐴) = 𝐴

Syntax hints:   = wceq 1534   ∈ wcel 2099  (class class class)co 7424   ℋchba 30852   +_ℎ cva 30853  0_ℎc0v 30857

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-9 2109  ax-ext 2697  ax-hvcom 30934  ax-hv0cl 30936  ax-hvaddid 30937

This theorem depends on definitions:  df-bi 206  df-an 395  df-ex 1775  df-cleq 2718

This theorem is referenced by:  hvsubeq0i  30996  hvaddcani  30998  hsn0elch  31181  hhssnv  31197  shscli  31250