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Theorem csbexa 3877
Description: The existence of proper substitution into a class. (Contributed by NM, 7-Aug-2007.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)
Hypotheses
Ref Expression
csbexa.1  _V
csbexa.2  _V
Assertion
Ref Expression
csbexa  [_  ]_  _V

Proof of Theorem csbexa
StepHypRef Expression
1 csbexa.1 . . 3  _V
2 csbexga 3876 . . 3  _V  _V  [_  ]_  _V
31, 2mpan 400 . 2  _V  [_  ]_  _V
4 csbexa.2 . 2  _V
53, 4mpg 1337 1  [_  ]_  _V
Colors of variables: wff set class
Syntax hints:  wal 1240   wcel 1390   _Vcvv 2551   [_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-bndl 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-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:  dfmpt2  5786
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