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Theorem csbex 3147
 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
csbex.1 A V
csbex.2 B V
Assertion
Ref Expression
csbex [A / x]B V

Proof of Theorem csbex
StepHypRef Expression
1 csbex.1 . . 3 A V
2 csbexg 3146 . . 3 ((A V x B V) → [A / x]B V)
31, 2mpan 651 . 2 (x B V → [A / x]B V)
4 csbex.2 . 2 B V
53, 4mpg 1548 1 [A / x]B V
 Colors of variables: wff setvar class Syntax hints:  ∀wal 1540   ∈ wcel 1710  Vcvv 2859  [csb 3136 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-sbc 3047  df-csb 3137 This theorem is referenced by: (None)
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