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Theorem wunin 9414
 Description: A weak universe is closed under intersections. (Contributed by Mario Carneiro, 2-Jan-2017.)
Hypotheses
Ref Expression
wununi.1 (𝜑𝑈 ∈ WUni)
wununi.2 (𝜑𝐴𝑈)
Assertion
Ref Expression
wunin (𝜑 → (𝐴𝐵) ∈ 𝑈)

Proof of Theorem wunin
StepHypRef Expression
1 wununi.1 . 2 (𝜑𝑈 ∈ WUni)
2 wununi.2 . 2 (𝜑𝐴𝑈)
3 inss1 3795 . . 3 (𝐴𝐵) ⊆ 𝐴
43a1i 11 . 2 (𝜑 → (𝐴𝐵) ⊆ 𝐴)
51, 2, 4wunss 9413 1 (𝜑 → (𝐴𝐵) ∈ 𝑈)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 1977   ∩ cin 3539   ⊆ wss 3540  WUnicwun 9401 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  ax-sep 4709 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  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-ne 2782  df-ral 2901  df-rex 2902  df-v 3175  df-in 3547  df-ss 3554  df-pw 4110  df-uni 4373  df-tr 4681  df-wun 9403 This theorem is referenced by:  wunress  15767
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