Theorem hvaddid2i 28812

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 28806	. 2 ⊢ (𝐴 ∈ ℋ → (0ℎ +ℎ 𝐴) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (0ℎ +ℎ 𝐴) = 𝐴

Syntax hints:   = wceq 1538   ∈ wcel 2111  (class class class)co 7135   ℋchba 28702   +_ℎ cva 28703  0_ℎc0v 28707

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-9 2121  ax-ext 2770  ax-hvcom 28784  ax-hv0cl 28786  ax-hvaddid 28787

This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-cleq 2791

This theorem is referenced by:  hvsubeq0i  28846  hvaddcani  28848  hsn0elch  29031  hhssnv  29047  shscli  29100