Theorem hvaddlidi 31048

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 31042	. 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 7431   ℋchba 30938   +_ℎ cva 30939  0_ℎc0v 30943

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 2708  ax-hvcom 31020  ax-hv0cl 31022  ax-hvaddid 31023

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-cleq 2729

This theorem is referenced by:  hvsubeq0i  31082  hvaddcani  31084  hsn0elch  31267  hhssnv  31283  shscli  31336