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Theorem vtocle 2600
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 2597 . 2 (A V → φ)
41, 3ax-mp 7 1 φ
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1226   wcel 1370  Vcvv 2531
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 1312  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-4 1377  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-ext 2000
This theorem depends on definitions:  df-bi 110  df-sb 1624  df-clab 2005  df-cleq 2011  df-clel 2014  df-v 2533
This theorem is referenced by:  repizf2  3885
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