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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 2713. (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 3496 . 2 𝑥 𝑥 = 𝐴
41, 3exlimiiv 1929 1 𝜑
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1537  wcel 2106  Vcvv 3478
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1777  df-clel 2814
This theorem is referenced by:  vtocl  3558  zfrepclf  5297  tz6.12i  6935  eloprabga  7541  eloprabgaOLD  7542  cfflb  10297  axcc3  10476  nn0ind-raph  12716  finxpreclem6  37379  tworepnotupword  46840
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