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Theorem elin1d 3785
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 3782 . 2 (𝑋 ∈ (𝐴𝐵) → 𝑋𝐴)
31, 2syl 17 1 (𝜑𝑋𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 1992  cin 3559
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1841  ax-6 1890  ax-7 1937  ax-9 2001  ax-10 2021  ax-11 2036  ax-12 2049  ax-13 2250  ax-ext 2606
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1883  df-clab 2613  df-cleq 2619  df-clel 2622  df-nfc 2756  df-v 3193  df-in 3567
This theorem is referenced by:  nmoleub2lem3  22818  nmoleub3  22822  tayl0  24015  esum2d  29928  ispisys2  29989  sigapisys  29991  sigapildsyslem  29997  sigapildsys  29998
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