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Theorem hvaddid2 21716
Description: Addition with the zero vector. (Contributed by NM, 18-Oct-1999.) (New usage is discouraged.)
Assertion
Ref Expression
hvaddid2  |-  ( A  e.  ~H  ->  ( 0h  +h  A )  =  A )

Proof of Theorem hvaddid2
StepHypRef Expression
1 ax-hv0cl 21697 . . 3  |-  0h  e.  ~H
2 ax-hvcom 21695 . . 3  |-  ( ( A  e.  ~H  /\  0h  e.  ~H )  -> 
( A  +h  0h )  =  ( 0h  +h  A ) )
31, 2mpan2 652 . 2  |-  ( A  e.  ~H  ->  ( A  +h  0h )  =  ( 0h  +h  A
) )
4 ax-hvaddid 21698 . 2  |-  ( A  e.  ~H  ->  ( A  +h  0h )  =  A )
53, 4eqtr3d 2392 1  |-  ( A  e.  ~H  ->  ( 0h  +h  A )  =  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1642    e. wcel 1710  (class class class)co 5945   ~Hchil 21613    +h cva 21614   0hc0v 21618
This theorem is referenced by:  hv2neg  21721  hvaddid2i  21722  hvaddsub4  21771  hilablo  21853  hilid  21854  shunssi  22061  spanunsni  22272  5oalem2  22348  3oalem2  22356
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2339  ax-hvcom 21695  ax-hv0cl 21697  ax-hvaddid 21698
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-cleq 2351
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