Theorem hvaddid2i 29292

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 29286	. 2 ⊢ (𝐴 ∈ ℋ → (0ℎ +ℎ 𝐴) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (0ℎ +ℎ 𝐴) = 𝐴

Syntax hints:   = wceq 1539   ∈ wcel 2108  (class class class)co 7255   ℋchba 29182   +_ℎ cva 29183  0_ℎc0v 29187

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-9 2118  ax-ext 2709  ax-hvcom 29264  ax-hv0cl 29266  ax-hvaddid 29267

This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1784  df-cleq 2730

This theorem is referenced by:  hvsubeq0i  29326  hvaddcani  29328  hsn0elch  29511  hhssnv  29527  shscli  29580