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Theorem hvaddid2 21602
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 21583 . . 3  |-  0h  e.  ~H
2 ax-hvcom 21581 . . 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 21584 . 2  |-  ( A  e.  ~H  ->  ( A  +h  0h )  =  A )
53, 4eqtr3d 2317 1  |-  ( A  e.  ~H  ->  ( 0h  +h  A )  =  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1623    e. wcel 1684  (class class class)co 5858   ~Hchil 21499    +h cva 21500   0hc0v 21504
This theorem is referenced by:  hv2neg  21607  hvaddid2i  21608  hvaddsub4  21657  hilablo  21739  hilid  21740  shunssi  21947  spanunsni  22158  5oalem2  22234  3oalem2  22242
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-11 1715  ax-ext 2264  ax-hvcom 21581  ax-hv0cl 21583  ax-hvaddid 21584
This theorem depends on definitions:  df-bi 177  df-an 360  df-cleq 2276
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