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Theorem spcegf 2935
 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 1793 . . . 4
4 spcgf.3 . . . . 5
54notbid 285 . . . 4
61, 3, 5spcgf 2934 . . 3
76con2d 107 . 2
8 df-ex 1542 . 2
97, 8syl6ibr 218 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 176  wal 1540  wex 1541  wnf 1544   wceq 1642   wcel 1710  wnfc 2476 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861 This theorem is referenced by:  spcegv  2940  rspce  2950
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