Theorem hvaddlidi 30956

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 30950	. 2 ⊢ (𝐴 ∈ ℋ → (0ℎ +ℎ 𝐴) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (0ℎ +ℎ 𝐴) = 𝐴

Syntax hints:   = wceq 1540   ∈ wcel 2108  (class class class)co 7403   ℋchba 30846   +_ℎ cva 30847  0_ℎc0v 30851

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 2007  ax-9 2118  ax-ext 2707  ax-hvcom 30928  ax-hv0cl 30930  ax-hvaddid 30931

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-cleq 2727

This theorem is referenced by:  hvsubeq0i  30990  hvaddcani  30992  hsn0elch  31175  hhssnv  31191  shscli  31244