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Theorem csb2 2848
 Description: Alternate expression for the proper substitution into a class, without referencing substitution into a wff. Note that x can be free in B but cannot occur in A. (Contributed by NM, 2-Dec-2013.)
Assertion
Ref Expression
csb2 A / xB = {yx(x = A y B)}
Distinct variable groups:   x,y,A   y,B
Allowed substitution hint:   B(x)

Proof of Theorem csb2
StepHypRef Expression
1 df-csb 2847 . 2 A / xB = {y[A / x]y B}
2 sbc5 2781 . . 3 ([A / x]y Bx(x = A y B))
32abbii 2150 . 2 {y[A / x]y B} = {yx(x = A y B)}
41, 3eqtri 2057 1 A / xB = {yx(x = A y B)}
 Colors of variables: wff set class Syntax hints:   ∧ wa 97   = wceq 1242  ∃wex 1378   ∈ wcel 1390  {cab 2023  [wsbc 2758  ⦋csb 2846 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-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-sbc 2759  df-csb 2847 This theorem is referenced by: (None)
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