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Theorem spcegf 3176
 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 1887 . . . 4
4 spcgf.3 . . . . 5
54notbid 294 . . . 4
61, 3, 5spcgf 3175 . . 3
76con2d 115 . 2
8 df-ex 1600 . 2
97, 8syl6ibr 227 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 184  wal 1381   wceq 1383  wex 1599  wnf 1603   wcel 1804  wnfc 2591 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-v 3097 This theorem is referenced by:  spcegv  3181  rspce  3191  euotd  4738  rspcegf  31352  stoweidlem36  31707  stoweidlem46  31717  bnj607  33707  bnj1491  33846
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