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Theorem vtocle 3255
 Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 9-Sep-1993.)
Hypotheses
Ref Expression
vtocle.1 𝐴 ∈ V
vtocle.2 (𝑥 = 𝐴𝜑)
Assertion
Ref Expression
vtocle 𝜑
Distinct variable groups:   𝑥,𝐴   𝜑,𝑥

Proof of Theorem vtocle
StepHypRef Expression
1 vtocle.1 . 2 𝐴 ∈ V
2 vtocle.2 . . 3 (𝑥 = 𝐴𝜑)
32vtocleg 3252 . 2 (𝐴 ∈ V → 𝜑)
41, 3ax-mp 5 1 𝜑
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1475   ∈ wcel 1977  Vcvv 3173 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-an 385  df-tru 1478  df-ex 1696  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-v 3175 This theorem is referenced by:  zfrepclf  4705  tz6.12i  6124  eloprabga  6645  cfflb  8964  axcc3  9143  nn0ind-raph  11353  finxpreclem6  32409
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