Theorem hvaddid2i 28441

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 28435	. 2 ⊢ (𝐴 ∈ ℋ → (0ℎ +ℎ 𝐴) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (0ℎ +ℎ 𝐴) = 𝐴

Syntax hints:   = wceq 1658   ∈ wcel 2166  (class class class)co 6905   ℋchba 28331   +_ℎ cva 28332  0_ℎc0v 28336

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-9 2175  ax-ext 2803  ax-hvcom 28413  ax-hv0cl 28415  ax-hvaddid 28416

This theorem depends on definitions:  df-bi 199  df-an 387  df-ex 1881  df-cleq 2818

This theorem is referenced by:  hvsubeq0i  28475  hvaddcani  28477  hsn0elch  28660  hhssnv  28676  shscli  28731