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Theorem hvaddid2 22530
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 22511 . . 3  |-  0h  e.  ~H
2 ax-hvcom 22509 . . 3  |-  ( ( A  e.  ~H  /\  0h  e.  ~H )  -> 
( A  +h  0h )  =  ( 0h  +h  A ) )
31, 2mpan2 654 . 2  |-  ( A  e.  ~H  ->  ( A  +h  0h )  =  ( 0h  +h  A
) )
4 ax-hvaddid 22512 . 2  |-  ( A  e.  ~H  ->  ( A  +h  0h )  =  A )
53, 4eqtr3d 2472 1  |-  ( A  e.  ~H  ->  ( 0h  +h  A )  =  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1653    e. wcel 1726  (class class class)co 6084   ~Hchil 22427    +h cva 22428   0hc0v 22432
This theorem is referenced by:  hv2neg  22535  hvaddid2i  22536  hvaddsub4  22585  hilablo  22667  hilid  22668  shunssi  22875  spanunsni  23086  5oalem2  23162  3oalem2  23170
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-11 1762  ax-ext 2419  ax-hvcom 22509  ax-hv0cl 22511  ax-hvaddid 22512
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-cleq 2431
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