Theorem hvaddlidi 31232

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 31226	. 2 ⊢ (𝐴 ∈ ℋ → (0ℎ +ℎ 𝐴) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (0ℎ +ℎ 𝐴) = 𝐴

Syntax hints:   = wceq 1560   ∈ wcel 2142  (class class class)co 7396   ℋchba 31122   +_ℎ cva 31123  0_ℎc0v 31127

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1815  ax-4 1829  ax-5 1930  ax-6 1987  ax-7 2028  ax-9 2152  ax-ext 2734  ax-hvcom 31204  ax-hv0cl 31206  ax-hvaddid 31207

This theorem depends on definitions:  df-bi 209  df-an 400  df-ex 1800  df-cleq 2754

This theorem is referenced by:  hvsubeq0i  31266  hvaddcani  31268  hsn0elch  31451  hhssnv  31467  shscli  31520