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Theorem csbiegf 2884
Description: Conversion of implicit substitution to explicit substitution into a class. (Contributed by NM, 11-Nov-2005.) (Revised by Mario Carneiro, 13-Oct-2016.)
Hypotheses
Ref Expression
csbiegf.1  V  F/_ C
csbiegf.2  C
Assertion
Ref Expression
csbiegf  V  [_  ]_  C
Distinct variable groups:   ,   , V
Allowed substitution hints:   ()    C()

Proof of Theorem csbiegf
StepHypRef Expression
1 csbiegf.2 . . 3  C
21ax-gen 1335 . 2  C
3 csbiegf.1 . . 3  V  F/_ C
4 csbiebt 2880 . . 3  V  F/_ C  C  [_  ]_  C
53, 4mpdan 398 . 2  V  C  [_  ]_  C
62, 5mpbii 136 1  V  [_  ]_  C
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98  wal 1240   wceq 1242   wcel 1390   F/_wnfc 2162   [_csb 2846
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-sbc 2759  df-csb 2847
This theorem is referenced by:  csbief  2885  sbcco3g  2897  csbco3g  2898  fmptcof  5274  fmpt2co  5779
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