Theorem hvaddlidi 30282

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 30276	. 2 ⊢ (𝐴 ∈ ℋ → (0ℎ +ℎ 𝐴) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (0ℎ +ℎ 𝐴) = 𝐴

Syntax hints:   = wceq 1542   ∈ wcel 2107  (class class class)co 7409   ℋchba 30172   +_ℎ cva 30173  0_ℎc0v 30177

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-9 2117  ax-ext 2704  ax-hvcom 30254  ax-hv0cl 30256  ax-hvaddid 30257

This theorem depends on definitions:  df-bi 206  df-an 398  df-ex 1783  df-cleq 2725

This theorem is referenced by:  hvsubeq0i  30316  hvaddcani  30318  hsn0elch  30501  hhssnv  30517  shscli  30570