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Theorem sbciedf 2850
 Description: Conversion of implicit substitution to explicit class substitution, deduction form. (Contributed by NM, 29-Dec-2014.)
Hypotheses
Ref Expression
sbcied.1
sbcied.2
sbciedf.3
sbciedf.4
Assertion
Ref Expression
sbciedf
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem sbciedf
StepHypRef Expression
1 sbcied.1 . 2
2 sbciedf.4 . 2
3 sbciedf.3 . . 3
4 sbcied.2 . . . 4
54ex 113 . . 3
63, 5alrimi 1456 . 2
7 sbciegft 2845 . 2
81, 2, 6, 7syl3anc 1170 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103  wal 1283   wceq 1285  wnf 1390   wcel 1434  wsbc 2816 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-sbc 2817 This theorem is referenced by:  sbcied  2851  sbc2iegf  2885  csbiebt  2943  sbcnestgf  2954  ovmpt2dxf  5657
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