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Theorem elin2d 3765
 Description: Elementhood in the first set of an intersection - deduction version. (Contributed by Thierry Arnoux, 3-May-2020.)
Hypothesis
Ref Expression
elin1d.1 (𝜑𝑋 ∈ (𝐴𝐵))
Assertion
Ref Expression
elin2d (𝜑𝑋𝐵)

Proof of Theorem elin2d
StepHypRef Expression
1 elin1d.1 . 2 (𝜑𝑋 ∈ (𝐴𝐵))
2 elinel2 3762 . 2 (𝑋 ∈ (𝐴𝐵) → 𝑋𝐵)
31, 2syl 17 1 (𝜑𝑋𝐵)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 1977   ∩ cin 3539 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-v 3175  df-in 3547 This theorem is referenced by:  bitsinv1  15002  txkgen  21265  nmoleub2lem3  22723  nmoleub3  22727  tayl0  23920  esum2d  29482  ispisys2  29543  sigapisys  29545  sigapildsyslem  29551  sigapildsys  29552  hoiqssbllem3  39514  smflimlem3  39659
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