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Theorem hvaddid2i 22533
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 22527 . 2  |-  ( A  e.  ~H  ->  ( 0h  +h  A )  =  A )
31, 2ax-mp 8 1  |-  ( 0h 
+h  A )  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1653    e. wcel 1726  (class class class)co 6083   ~Hchil 22424    +h cva 22425   0hc0v 22429
This theorem is referenced by:  hvsubeq0i  22567  hvaddcani  22569  hsn0elch  22752  hhssnv  22766  shscli  22821
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-11 1762  ax-ext 2419  ax-hvcom 22506  ax-hv0cl 22508  ax-hvaddid 22509
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-cleq 2431
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