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Theorem difidALT 3923
 Description: Alternate proof of difid 3922. (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 3564 . 2 (𝐴𝐴) = {𝑥𝐴 ∣ ¬ 𝑥𝐴}
2 dfnul3 3894 . 2 ∅ = {𝑥𝐴 ∣ ¬ 𝑥𝐴}
31, 2eqtr4i 2646 1 (𝐴𝐴) = ∅
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   = wceq 1480   ∈ wcel 1987  {crab 2911   ∖ cdif 3552  ∅c0 3891 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601 This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-rab 2916  df-v 3188  df-dif 3558  df-nul 3892 This theorem is referenced by: (None)
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