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Theorem spcegf 3024
 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 1811 . . . 4
4 spcgf.3 . . . . 5
54notbid 286 . . . 4
61, 3, 5spcgf 3023 . . 3
76con2d 109 . 2
8 df-ex 1551 . 2
97, 8syl6ibr 219 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177  wal 1549  wex 1550  wnf 1553   wceq 1652   wcel 1725  wnfc 2558 This theorem is referenced by:  spcegv  3029  rspce  3039  euotd  4449  rspcegf  27651  stoweidlem36  27742  stoweidlem46  27752  bnj607  29214  bnj1491  29353 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950
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