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Theorem difidALT 3903
Description: Alternate proof of difid 3902. (Contributed by David Abernethy, 17-Jun-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
difidALT (𝐴𝐴) = ∅

Proof of Theorem difidALT
Dummy variable 𝑥 is distinct from all other variables.
StepHypRef Expression
1 dfdif2 3549 . 2 (𝐴𝐴) = {𝑥𝐴 ∣ ¬ 𝑥𝐴}
2 dfnul3 3877 . 2 ∅ = {𝑥𝐴 ∣ ¬ 𝑥𝐴}
31, 2eqtr4i 2635 1 (𝐴𝐴) = ∅
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3   = wceq 1475  wcel 1977  {crab 2900  cdif 3537  c0 3874
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590
This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-rab 2905  df-v 3175  df-dif 3543  df-nul 3875
This theorem is referenced by: (None)
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