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Theorem vtocle 2621
 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 2618 . 2 (A V → φ)
41, 3ax-mp 7 1 φ
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1242   ∈ wcel 1390  Vcvv 2551 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-v 2553 This theorem is referenced by:  repizf2  3906  nn0ind-raph  8111
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