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Theorem spcegf 3190
Description: Existential specialization, using implicit substitution. (Contributed by NM, 2-Feb-1997.)
Hypotheses
Ref Expression
spcgf.1
spcgf.2
spcgf.3
Assertion
Ref Expression
spcegf

Proof of Theorem spcegf
StepHypRef Expression
1 spcgf.1 . . . 4
2 spcgf.2 . . . . 5
32nfn 1901 . . . 4
4 spcgf.3 . . . . 5
54notbid 294 . . . 4
61, 3, 5spcgf 3189 . . 3
76con2d 115 . 2
8 df-ex 1613 . 2
97, 8syl6ibr 227 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  A.wal 1393  =wceq 1395  E.wex 1612  F/wnf 1616  e.wcel 1818  F/_wnfc 2605
This theorem is referenced by:  spcegv  3195  rspce  3205  euotd  4753  rspcegf  31398  stoweidlem36  31818  stoweidlem46  31828  bnj607  33974  bnj1491  34113
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-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-v 3111
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