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Theorem elin1d 3835
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
elin1d (𝜑𝑋𝐴)

Proof of Theorem elin1d
StepHypRef Expression
1 elin1d.1 . 2 (𝜑𝑋 ∈ (𝐴𝐵))
2 elinel1 3832 . 2 (𝑋 ∈ (𝐴𝐵) → 𝑋𝐴)
31, 2syl 17 1 (𝜑𝑋𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2030  cin 3606
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-v 3233  df-in 3614
This theorem is referenced by:  nmoleub2lem3  22961  nmoleub3  22965  tayl0  24161  esum2d  30283  ispisys2  30344  sigapisys  30346  sigapildsyslem  30352  sigapildsys  30353  eulerpartlemgvv  30566  tgoldbachgt  30869
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