Theorem hvaddlidi 31118

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 31112	. 2 ⊢ (𝐴 ∈ ℋ → (0ℎ +ℎ 𝐴) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (0ℎ +ℎ 𝐴) = 𝐴

Syntax hints:   = wceq 1542   ∈ wcel 2114  (class class class)co 7361   ℋchba 31008   +_ℎ cva 31009  0_ℎc0v 31013

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-9 2124  ax-ext 2709  ax-hvcom 31090  ax-hv0cl 31092  ax-hvaddid 31093

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1782  df-cleq 2729

This theorem is referenced by:  hvsubeq0i  31152  hvaddcani  31154  hsn0elch  31337  hhssnv  31353  shscli  31406