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Theorem hvaddid2 22478
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 22459 . . 3  |-  0h  e.  ~H
2 ax-hvcom 22457 . . 3  |-  ( ( A  e.  ~H  /\  0h  e.  ~H )  -> 
( A  +h  0h )  =  ( 0h  +h  A ) )
31, 2mpan2 653 . 2  |-  ( A  e.  ~H  ->  ( A  +h  0h )  =  ( 0h  +h  A
) )
4 ax-hvaddid 22460 . 2  |-  ( A  e.  ~H  ->  ( A  +h  0h )  =  A )
53, 4eqtr3d 2438 1  |-  ( A  e.  ~H  ->  ( 0h  +h  A )  =  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1649    e. wcel 1721  (class class class)co 6040   ~Hchil 22375    +h cva 22376   0hc0v 22380
This theorem is referenced by:  hv2neg  22483  hvaddid2i  22484  hvaddsub4  22533  hilablo  22615  hilid  22616  shunssi  22823  spanunsni  23034  5oalem2  23110  3oalem2  23118
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-11 1757  ax-ext 2385  ax-hvcom 22457  ax-hv0cl 22459  ax-hvaddid 22460
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548  df-cleq 2397
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