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Theorem vtocle 2760
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 2757 . 2 (𝐴 ∈ V → 𝜑)
41, 3ax-mp 5 1 𝜑
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1331  wcel 1480  Vcvv 2686
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-v 2688
This theorem is referenced by:  repizf2  4086  nn0ind-raph  9180
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