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Theorem spcgf 2635
 Description: Rule of specialization, using implicit substitution. Compare Theorem 7.3 of [Quine] p. 44. (Contributed by NM, 2-Feb-1997.) (Revised by Andrew Salmon, 12-Aug-2011.)
Hypotheses
Ref Expression
spcgf.1
spcgf.2
spcgf.3
Assertion
Ref Expression
spcgf

Proof of Theorem spcgf
StepHypRef Expression
1 spcgf.2 . . 3
2 spcgf.1 . . 3
31, 2spcgft 2630 . 2
4 spcgf.3 . 2
53, 4mpg 1340 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98  wal 1241   wceq 1243  wnf 1349   wcel 1393  wnfc 2165 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559 This theorem is referenced by:  spcgv  2640  rspc  2650  elabgt  2684  eusvnf  4185  mpt2fvex  5829
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