Theorem hvaddlidi 31104

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 31098	. 2 ⊢ (𝐴 ∈ ℋ → (0ℎ +ℎ 𝐴) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (0ℎ +ℎ 𝐴) = 𝐴

Syntax hints:   = wceq 1541   ∈ wcel 2113  (class class class)co 7358   ℋchba 30994   +_ℎ cva 30995  0_ℎc0v 30999

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-9 2123  ax-ext 2708  ax-hvcom 31076  ax-hv0cl 31078  ax-hvaddid 31079

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1781  df-cleq 2728

This theorem is referenced by:  hvsubeq0i  31138  hvaddcani  31140  hsn0elch  31323  hhssnv  31339  shscli  31392