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Theorem vtocle 3555
Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 9-Sep-1993.) Avoid df-clab 2715. (Revised by Wolf Lammen, 31-May-2025.)
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.2 . 2 (𝑥 = 𝐴𝜑)
2 vtocle.1 . . 3 𝐴 ∈ V
32isseti 3498 . 2 𝑥 𝑥 = 𝐴
41, 3exlimiiv 1931 1 𝜑
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1540  wcel 2108  Vcvv 3480
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-clel 2816
This theorem is referenced by:  vtocl  3558  zfrepclf  5291  tz6.12i  6934  eloprabga  7542  cfflb  10299  axcc3  10478  nn0ind-raph  12718  finxpreclem6  37397  ormkglobd  46890  tworepnotupword  46901
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