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Theorem sbccsbg 3164
 Description: Substitution into a wff expressed in terms of substitution into a class. (Contributed by NM, 15-Aug-2007.)
Assertion
Ref Expression
sbccsbg (A V → ([̣A / xφy [A / x]{y φ}))
Distinct variable group:   x,y
Allowed substitution hints:   φ(x,y)   A(x,y)   V(x,y)

Proof of Theorem sbccsbg
StepHypRef Expression
1 abid 2341 . . 3 (y {y φ} ↔ φ)
21sbcbii 3101 . 2 ([̣A / xy {y φ} ↔ [̣A / xφ)
3 sbcel2g 3157 . 2 (A V → ([̣A / xy {y φ} ↔ y [A / x]{y φ}))
42, 3syl5bbr 250 1 (A V → ([̣A / xφy [A / x]{y φ}))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   ∈ wcel 1710  {cab 2339  [̣wsbc 3046  [csb 3136 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-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  df-csb 3137 This theorem is referenced by: (None)
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