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Theorem vtocl 2602
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 1418 . 2 xψ
2 vtocl.1 . 2 A V
3 vtocl.2 . 2 (x = A → (φψ))
4 vtocl.3 . 2 φ
51, 2, 3, 4vtoclf 2601 1 ψ
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98   = wceq 1242   wcel 1390  Vcvv 2551
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 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-v 2553
This theorem is referenced by:  vtoclb  2605  zfauscl  3868  bnd2  3917  pwex  3923  uniex  4140  ordtriexmid  4210  onsucsssucexmid  4212  regexmid  4219  ordsoexmid  4240  nnregexmid  4285  acexmidlemv  5453  caovcan  5607  bj-uniex  9348  bj-omtrans  9390
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