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Theorem difexi 4736
 Description: Existence of a difference, inference version of difexg 4735. (Contributed by Glauco Siliprandi, 3-Mar-2021.) (Revised by AV, 26-Mar-2021.)
Hypothesis
Ref Expression
difexi.1 𝐴 ∈ V
Assertion
Ref Expression
difexi (𝐴𝐵) ∈ V

Proof of Theorem difexi
StepHypRef Expression
1 difexi.1 . 2 𝐴 ∈ V
2 difexg 4735 . 2 (𝐴 ∈ V → (𝐴𝐵) ∈ V)
31, 2ax-mp 5 1 (𝐴𝐵) ∈ V
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 1977  Vcvv 3173   ∖ cdif 3537 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  ax-sep 4709 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-v 3175  df-dif 3543  df-in 3547  df-ss 3554 This theorem is referenced by:  marypha1lem  8222  inf3lem3  8410  setindtr  36609  clsk3nimkb  37358  meaiuninclem  39373  meaiininclem  39376  upgrres1lem1  40528  nbgrval  40560
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