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Theorem vtoclef 2927
 Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 18-Aug-1993.)
Hypotheses
Ref Expression
vtoclef.1 xφ
vtoclef.2 A V
vtoclef.3 (x = Aφ)
Assertion
Ref Expression
vtoclef φ
Distinct variable group:   x,A
Allowed substitution hint:   φ(x)

Proof of Theorem vtoclef
StepHypRef Expression
1 vtoclef.2 . . 3 A V
21isseti 2865 . 2 x x = A
3 vtoclef.1 . . 3 xφ
4 vtoclef.3 . . 3 (x = Aφ)
53, 4exlimi 1803 . 2 (x x = Aφ)
62, 5ax-mp 5 1 φ
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∃wex 1541  Ⅎwnf 1544   = wceq 1642   ∈ wcel 1710  Vcvv 2859 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-v 2861 This theorem is referenced by: (None)
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