Theorem hvaddlidi 30965

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 30959	. 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 7390   ℋchba 30855   +_ℎ cva 30856  0_ℎc0v 30860

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 2702  ax-hvcom 30937  ax-hv0cl 30939  ax-hvaddid 30940

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-cleq 2722

This theorem is referenced by:  hvsubeq0i  30999  hvaddcani  31001  hsn0elch  31184  hhssnv  31200  shscli  31253