Theorem hvaddlidi 31008

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 31002	. 2 ⊢ (𝐴 ∈ ℋ → (0ℎ +ℎ 𝐴) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (0ℎ +ℎ 𝐴) = 𝐴

Syntax hints:   = wceq 1540   ∈ wcel 2109  (class class class)co 7369   ℋchba 30898   +_ℎ cva 30899  0_ℎc0v 30903

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-9 2119  ax-ext 2701  ax-hvcom 30980  ax-hv0cl 30982  ax-hvaddid 30983

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-cleq 2721

This theorem is referenced by:  hvsubeq0i  31042  hvaddcani  31044  hsn0elch  31227  hhssnv  31243  shscli  31296