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Theorem csb2 3138
 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 / x]B = {y x(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 3137 . 2 [A / x]B = {y A / xy B}
2 sbc5 3070 . . 3 ([̣A / xy Bx(x = A y B))
32abbii 2465 . 2 {y A / xy B} = {y x(x = A y B)}
41, 3eqtri 2373 1 [A / x]B = {y x(x = A y B)}
 Colors of variables: wff setvar class Syntax hints:   ∧ wa 358  ∃wex 1541   = wceq 1642   ∈ 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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