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Theorem difexd 39471
 Description: Existence of a difference. (Contributed by SN, 16-Jul-2024.)
Hypothesis
Ref Expression
difexd.1 (𝜑𝐴𝑉)
Assertion
Ref Expression
difexd (𝜑 → (𝐴𝐵) ∈ V)

Proof of Theorem difexd
StepHypRef Expression
1 difexd.1 . 2 (𝜑𝐴𝑉)
2 difexg 5198 . 2 (𝐴𝑉 → (𝐴𝐵) ∈ V)
31, 2syl 17 1 (𝜑 → (𝐴𝐵) ∈ V)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 2111  Vcvv 3441   ∖ cdif 3879 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-8 2113  ax-9 2121  ax-ext 2770  ax-sep 5170 This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1541  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-rab 3115  df-v 3443  df-dif 3885  df-in 3889  df-ss 3899 This theorem is referenced by:  fsuppssind  39543
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