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Theorem sbcex 3055
 Description: By our definition of proper substitution, it can only be true if the substituted expression is a set. (Contributed by Mario Carneiro, 13-Oct-2016.)
Assertion
Ref Expression
sbcex ([̣A / xφA V)

Proof of Theorem sbcex
StepHypRef Expression
1 df-sbc 3047 . 2 ([̣A / xφA {x φ})
2 elex 2867 . 2 (A {x φ} → A V)
31, 2sylbi 187 1 ([̣A / xφA V)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 1710  {cab 2339  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-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  df-sbc 3047 This theorem is referenced by:  sbcco  3068  sbc5  3070  sbcan  3088  sbcor  3090  sbcal  3093  sbcex2  3095  spesbc  3127  opelopabsb  4697
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