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Theorem elin2d 3795
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 3792 . 2 (𝑋 ∈ (𝐴𝐵) → 𝑋𝐵)
31, 2syl 17 1 (𝜑𝑋𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 1988  cin 3566
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-9 1997  ax-10 2017  ax-11 2032  ax-12 2045  ax-13 2244  ax-ext 2600
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1484  df-ex 1703  df-nf 1708  df-sb 1879  df-clab 2607  df-cleq 2613  df-clel 2616  df-nfc 2751  df-v 3197  df-in 3574
This theorem is referenced by:  bitsinv1  15145  txkgen  21436  nmoleub2lem3  22896  nmoleub3  22900  tayl0  24097  esum2d  30129  ispisys2  30190  sigapisys  30192  sigapildsyslem  30198  sigapildsys  30199  tgoldbachgt  30715  bnj1172  31043  hoiqssbllem3  40601  smflimlem3  40744
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