Theorem hvaddid2i 29678

Description: Addition with the zero vector. (Contributed by NM, 18-Aug-1999.) (New usage is discouraged.)

Hypothesis

Ref	Expression
hvaddid2.1	⊢ 𝐴 ∈ ℋ

Assertion

Ref	Expression
hvaddid2i	⊢ (0ℎ +ℎ 𝐴) = 𝐴

Proof of Theorem hvaddid2i

Step	Hyp	Ref	Expression
1		hvaddid2.1	. 2 ⊢ 𝐴 ∈ ℋ
2		hvaddid2 29672	. 2 ⊢ (𝐴 ∈ ℋ → (0ℎ +ℎ 𝐴) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (0ℎ +ℎ 𝐴) = 𝐴

Syntax hints:   = wceq 1541   ∈ wcel 2106  (class class class)co 7341   ℋchba 29568   +_ℎ cva 29569  0_ℎc0v 29573

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 1913  ax-6 1971  ax-7 2011  ax-9 2116  ax-ext 2708  ax-hvcom 29650  ax-hv0cl 29652  ax-hvaddid 29653

This theorem depends on definitions:  df-bi 206  df-an 398  df-ex 1782  df-cleq 2729

This theorem is referenced by:  hvsubeq0i  29712  hvaddcani  29714  hsn0elch  29897  hhssnv  29913  shscli  29966