Theorem hvaddid2i 28798

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 28792	. 2 ⊢ (𝐴 ∈ ℋ → (0ℎ +ℎ 𝐴) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (0ℎ +ℎ 𝐴) = 𝐴

Syntax hints:   = wceq 1531   ∈ wcel 2108  (class class class)co 7148   ℋchba 28688   +_ℎ cva 28689  0_ℎc0v 28693

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 1905  ax-6 1964  ax-7 2009  ax-9 2118  ax-ext 2791  ax-hvcom 28770  ax-hv0cl 28772  ax-hvaddid 28773

This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1775  df-cleq 2812

This theorem is referenced by:  hvsubeq0i  28832  hvaddcani  28834  hsn0elch  29017  hhssnv  29033  shscli  29086