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Theorem s1val 13231
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 (𝐴𝑉 → ⟨“𝐴”⟩ = {⟨0, 𝐴⟩})

Proof of Theorem s1val
StepHypRef Expression
1 df-s1 13157 . 2 ⟨“𝐴”⟩ = {⟨0, ( I ‘𝐴)⟩}
2 fvi 6165 . . . 4 (𝐴𝑉 → ( I ‘𝐴) = 𝐴)
32opeq2d 4347 . . 3 (𝐴𝑉 → ⟨0, ( I ‘𝐴)⟩ = ⟨0, 𝐴⟩)
43sneqd 4137 . 2 (𝐴𝑉 → {⟨0, ( I ‘𝐴)⟩} = {⟨0, 𝐴⟩})
51, 4syl5eq 2656 1 (𝐴𝑉 → ⟨“𝐴”⟩ = {⟨0, 𝐴⟩})
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1475  wcel 1977  {csn 4125  cop 4131   I cid 4948  cfv 5804  0cc0 9815  ⟨“cs1 13149
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-9 1986  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590  ax-sep 4709  ax-nul 4717  ax-pr 4833
This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-eu 2462  df-mo 2463  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-ral 2901  df-rex 2902  df-rab 2905  df-v 3175  df-sbc 3403  df-dif 3543  df-un 3545  df-in 3547  df-ss 3554  df-nul 3875  df-if 4037  df-sn 4126  df-pr 4128  df-op 4132  df-uni 4373  df-br 4584  df-opab 4644  df-id 4953  df-xp 5044  df-rel 5045  df-cnv 5046  df-co 5047  df-dm 5048  df-iota 5768  df-fun 5806  df-fv 5812  df-s1 13157
This theorem is referenced by:  s1rn  13232  s1cl  13235  s1dmALT  13242  s1fv  13243  s111  13248  repsw1  13381  s1co  13430  s2prop  13502  ofs1  13557  gsumws1  17199  ofcs1  29947  signstf0  29971  uspgr1ewop  40474  usgr2v1e2w  40478  0wlkOns1  41289
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