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Theorem vtocl 2585
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 1402 . 2 xψ
2 vtocl.1 . 2 A V
3 vtocl.2 . 2 (x = A → (φψ))
4 vtocl.3 . 2 φ
51, 2, 3, 4vtoclf 2584 1 ψ
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98   = wceq 1228   wcel 1374  Vcvv 2535
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 1316  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-v 2537
This theorem is referenced by:  vtoclb  2588  zfauscl  3851  bnd2  3900  pwex  3906  uniex  4124  ordtriexmid  4194  onsucsssucexmid  4196  regexmid  4203  ordsoexmid  4224  nnregexmid  4269  acexmidlemv  5434  caovcan  5588  bj-uniex  7287  bj-omtrans  7325
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