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Theorem rspn0 3797
 Description: Specialization for restricted generalization with a nonempty set. (Contributed by Alexander van der Vekens, 6-Sep-2018.)
Assertion
Ref Expression
rspn0
Distinct variable groups:   ,   ,

Proof of Theorem rspn0
StepHypRef Expression
1 n0 3794 . 2
2 nfra1 2838 . . . 4
3 nfv 1707 . . . 4
42, 3nfim 1920 . . 3
5 rsp 2823 . . . 4
65com12 31 . . 3
74, 6exlimi 1912 . 2
81, 7sylbi 195 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  E.wex 1612  e.wcel 1818  =/=wne 2652  A.wral 2807   c0 3784 This theorem is referenced by:  hashge2el2dif  12521  scmatf1  19033  usgfiregdegfi  24911  ralralimp  32295 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-v 3111  df-dif 3478  df-nul 3785
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