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Theorem csbidmg 3190
 Description: Idempotent law for class substitutions. (Contributed by NM, 1-Mar-2008.)
Assertion
Ref Expression
csbidmg (A V[A / x][A / x]B = [A / x]B)
Distinct variable group:   x,A
Allowed substitution hints:   B(x)   V(x)

Proof of Theorem csbidmg
StepHypRef Expression
1 elex 2867 . 2 (A VA V)
2 csbnest1g 3188 . . 3 (A V → [A / x][A / x]B = [[A / x]A / x]B)
3 csbconstg 3150 . . . 4 (A V → [A / x]A = A)
43csbeq1d 3142 . . 3 (A V → [[A / x]A / x]B = [A / x]B)
52, 4eqtrd 2385 . 2 (A V → [A / x][A / x]B = [A / x]B)
61, 5syl 15 1 (A V[A / x][A / x]B = [A / x]B)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642   ∈ wcel 1710  Vcvv 2859  [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-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  df-csb 3137 This theorem is referenced by: (None)
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