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Theorem vtocle 3546
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 3516 . 2 (𝐴 ∈ V → 𝜑)
41, 3ax-mp 5 1 𝜑
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1542  wcel 2107  Vcvv 3447
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-clel 2811
This theorem is referenced by:  zfrepclf  5255  tz6.12i  6874  eloprabga  7468  eloprabgaOLD  7469  cfflb  10203  axcc3  10382  nn0ind-raph  12611  finxpreclem6  35917  tworepnotupword  45215
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