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Theorem spcegf 3048
 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 1835 . . . 4
4 spcgf.3 . . . . 5
54notbid 294 . . . 4
61, 3, 5spcgf 3047 . . 3
76con2d 115 . 2
8 df-ex 1587 . 2
97, 8syl6ibr 227 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 184  wal 1367   wceq 1369  wex 1586  wnf 1589   wcel 1756  wnfc 2561 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2419 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2969 This theorem is referenced by:  spcegv  3053  rspce  3063  euotd  4587  rspcegf  29698  stoweidlem36  29784  stoweidlem46  29794  bnj607  31796  bnj1491  31935
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