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Theorem difidALT 4288
 Description: Alternate proof of difid 4287. (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 3892 . 2 (𝐴𝐴) = {𝑥𝐴 ∣ ¬ 𝑥𝐴}
2 dfnul3 4249 . 2 ∅ = {𝑥𝐴 ∣ ¬ 𝑥𝐴}
31, 2eqtr4i 2824 1 (𝐴𝐴) = ∅
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   = wceq 1538   ∈ wcel 2111  {crab 3110   ∖ cdif 3880  ∅c0 4246 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-9 2121  ax-ext 2770 This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-rab 3115  df-dif 3886  df-nul 4247 This theorem is referenced by: (None)
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