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Theorem sbcieg 3078
 Description: Conversion of implicit substitution to explicit class substitution. (Contributed by NM, 10-Nov-2005.)
Hypothesis
Ref Expression
sbcieg.1 (x = A → (φψ))
Assertion
Ref Expression
sbcieg (A V → ([̣A / xφψ))
Distinct variable groups:   x,A   ψ,x
Allowed substitution hints:   φ(x)   V(x)

Proof of Theorem sbcieg
StepHypRef Expression
1 elex 2867 . 2 (A VA V)
2 nfv 1619 . . 3 xψ
3 sbcieg.1 . . 3 (x = A → (φψ))
42, 3sbciegf 3077 . 2 (A V → ([̣A / xφψ))
51, 4syl 15 1 (A V → ([̣A / xφψ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   = wceq 1642   ∈ wcel 1710  Vcvv 2859  [̣wsbc 3046 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-sbc 3047 This theorem is referenced by:  sbcie  3080  ralsng  3765  rexsng  3766
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