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Theorem wunres 10144
 Description: A weak universe is closed under restrictions. (Contributed by Mario Carneiro, 12-Jan-2017.)
Hypotheses
Ref Expression
wun0.1 (𝜑𝑈 ∈ WUni)
wunop.2 (𝜑𝐴𝑈)
Assertion
Ref Expression
wunres (𝜑 → (𝐴𝐵) ∈ 𝑈)

Proof of Theorem wunres
StepHypRef Expression
1 wun0.1 . 2 (𝜑𝑈 ∈ WUni)
2 wunop.2 . 2 (𝜑𝐴𝑈)
3 resss 5843 . . 3 (𝐴𝐵) ⊆ 𝐴
43a1i 11 . 2 (𝜑 → (𝐴𝐵) ⊆ 𝐴)
51, 2, 4wunss 10125 1 (𝜑 → (𝐴𝐵) ∈ 𝑈)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 2111   ⊆ wss 3881   ↾ cres 5521  WUnicwun 10113 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-11 2158  ax-ext 2770  ax-sep 5167 This theorem depends on definitions:  df-bi 210  df-an 400  df-3an 1086  df-tru 1541  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-ne 2988  df-ral 3111  df-rab 3115  df-v 3443  df-in 3888  df-ss 3898  df-pw 4499  df-uni 4801  df-tr 5137  df-res 5531  df-wun 10115 This theorem is referenced by:  wunsets  16518
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