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  1. ∃x ∀y R(x, y)                                 [Hypothesis]
  2.  
  3. Let c be a constant such that ∀y R(c, y)
  4.     ∀y R(c, y)    
  5.  
  6.     Given constant d:
  7.         R(c, d)                               [∀ elim]
  8.         ∃x R(x, d)                            [∃ intro]
  9.  
  10.     ∀y ∃x R(x, y)                             [∀ intro]
  11.  
  12. ∀y ∃x R(x, y)                                 [∃ elim]
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