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Theorem s1val 11681
Description: Value of a single-symbol word. (Contributed by Stefan O'Rear, 15-Aug-2015.) (Revised by Mario Carneiro, 26-Feb-2016.)
Assertion
Ref Expression
s1val  |-  ( A  e.  V  ->  <" A ">  =  { <. 0 ,  A >. } )

Proof of Theorem s1val
StepHypRef Expression
1 df-s1 11654 . 2  |-  <" A ">  =  { <. 0 ,  (  _I  `  A ) >. }
2 fvi 5724 . . . 4  |-  ( A  e.  V  ->  (  _I  `  A )  =  A )
32opeq2d 3935 . . 3  |-  ( A  e.  V  ->  <. 0 ,  (  _I  `  A
) >.  =  <. 0 ,  A >. )
43sneqd 3772 . 2  |-  ( A  e.  V  ->  { <. 0 ,  (  _I  `  A ) >. }  =  { <. 0 ,  A >. } )
51, 4syl5eq 2433 1  |-  ( A  e.  V  ->  <" A ">  =  { <. 0 ,  A >. } )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1649    e. wcel 1717   {csn 3759   <.cop 3762    _I cid 4436   ` cfv 5396   0cc0 8925   <"cs1 11648
This theorem is referenced by:  s1cl  11684  s1fv  11689  s111  11691  wrdexb  11692  s1co  11731  s2prop  11790  gsumws1  14714
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 1661  ax-8 1682  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2370  ax-sep 4273  ax-nul 4281  ax-pr 4346
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2244  df-mo 2245  df-clab 2376  df-cleq 2382  df-clel 2385  df-nfc 2514  df-ne 2554  df-ral 2656  df-rex 2657  df-rab 2660  df-v 2903  df-sbc 3107  df-dif 3268  df-un 3270  df-in 3272  df-ss 3279  df-nul 3574  df-if 3685  df-sn 3765  df-pr 3766  df-op 3768  df-uni 3960  df-br 4156  df-opab 4210  df-id 4441  df-xp 4826  df-rel 4827  df-cnv 4828  df-co 4829  df-dm 4830  df-iota 5360  df-fun 5398  df-fv 5404  df-s1 11654
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