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Theorem vtocleg 2925
 Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 10-Jan-2004.)
Hypothesis
Ref Expression
vtocleg.1 (x = Aφ)
Assertion
Ref Expression
vtocleg (A Vφ)
Distinct variable groups:   x,A   φ,x
Allowed substitution hint:   V(x)

Proof of Theorem vtocleg
StepHypRef Expression
1 elisset 2869 . 2 (A Vx x = A)
2 vtocleg.1 . . 3 (x = Aφ)
32exlimiv 1634 . 2 (x x = Aφ)
41, 3syl 15 1 (A Vφ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∃wex 1541   = wceq 1642   ∈ wcel 1710 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-11 1746  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-v 2861 This theorem is referenced by:  vtocle  2928  spsbc  3058  eloprabga  5578
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