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Theorem vtocl 2909
 Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 30-Aug-1993.)
Hypotheses
Ref Expression
vtocl.1 A V
vtocl.2 (x = A → (φψ))
vtocl.3 φ
Assertion
Ref Expression
vtocl ψ
Distinct variable groups:   x,A   ψ,x
Allowed substitution hint:   φ(x)

Proof of Theorem vtocl
StepHypRef Expression
1 nfv 1619 . 2 xψ
2 vtocl.1 . 2 A V
3 vtocl.2 . 2 (x = A → (φψ))
4 vtocl.3 . 2 φ
51, 2, 3, 4vtoclf 2908 1 ψ
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   = 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:  vtoclb  2912  caovcan  5628  enprmapc  6083
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