Theorem hvaddid2 5008

Description: Addition with the zero vector.

Hypothesis

Ref	Expression
hvaddid2.1	|- A e. H~

Assertion

Ref	Expression
hvaddid2	|- (0v +v A) = A

Proof of Theorem hvaddid2

Step	Hyp	Ref	Expression
1		hvaddid2.1	. 2 |- A e. H~
2		hvaddid2t 5003	. 2 |- (A e. H~ -> (0v +v A) = A)
3	1, 2	ax-mp 6	1 |- (0v +v A) = A

Syntax hints:   = wceq 1091   e. wcel 1092  (class class class)co 3001  H~chil 4958   +v cva 4959  0vc0v 4961

This theorem is referenced by:  hv2neg 5010  hvsubeq0 5035  hvaddcan 5037  hsn0elch 5155  shscl 5282

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-gen 677  ax-17 925  ax-ext 1074  ax-hvcom 4985  ax-hvzercl 4987  ax-hvaddid 4988

This theorem depends on definitions:  df-bi 128  df-an 198  df-cleq 1097

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