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Theorem hvaddid2i 25924
Description: Addition with the zero vector. (Contributed by NM, 18-Aug-1999.) (New usage is discouraged.)
Hypothesis
Ref Expression
hvaddid2.1  |-  A  e. 
~H
Assertion
Ref Expression
hvaddid2i  |-  ( 0h 
+h  A )  =  A

Proof of Theorem hvaddid2i
StepHypRef Expression
1 hvaddid2.1 . 2  |-  A  e. 
~H
2 hvaddid2 25918 . 2  |-  ( A  e.  ~H  ->  ( 0h  +h  A )  =  A )
31, 2ax-mp 5 1  |-  ( 0h 
+h  A )  =  A
Colors of variables: wff setvar class
Syntax hints:    = wceq 1383    e. wcel 1804  (class class class)co 6281   ~Hchil 25814    +h cva 25815   0hc0v 25819
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-ext 2421  ax-hvcom 25896  ax-hv0cl 25898  ax-hvaddid 25899
This theorem depends on definitions:  df-bi 185  df-an 371  df-cleq 2435
This theorem is referenced by:  hvsubeq0i  25958  hvaddcani  25960  hsn0elch  26144  hhssnv  26158  shscli  26213
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