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Theorem hvaddid2i 21624
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 21618 . 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 1632    e. wcel 1696  (class class class)co 5874   ~Hchil 21515    +h cva 21516   0hc0v 21520
This theorem is referenced by:  hvsubeq0i  21658  hvaddcani  21660  hsn0elch  21843  hhssnv  21857  shscli  21912
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-11 1727  ax-ext 2277  ax-hvcom 21597  ax-hv0cl 21599  ax-hvaddid 21600
This theorem depends on definitions:  df-bi 177  df-an 360  df-cleq 2289
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