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Theorem wundif 10214
Description: A weak universe is closed under class difference. (Contributed by Mario Carneiro, 2-Jan-2017.)
Hypotheses
Ref Expression
wununi.1 (𝜑𝑈 ∈ WUni)
wununi.2 (𝜑𝐴𝑈)
Assertion
Ref Expression
wundif (𝜑 → (𝐴𝐵) ∈ 𝑈)

Proof of Theorem wundif
StepHypRef Expression
1 wununi.1 . 2 (𝜑𝑈 ∈ WUni)
2 wununi.2 . 2 (𝜑𝐴𝑈)
3 difssd 4023 . 2 (𝜑 → (𝐴𝐵) ⊆ 𝐴)
41, 2, 3wunss 10212 1 (𝜑 → (𝐴𝐵) ∈ 𝑈)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2114  cdif 3840  WUnicwun 10200
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2020  ax-8 2116  ax-9 2124  ax-11 2162  ax-ext 2710  ax-sep 5167
This theorem depends on definitions:  df-bi 210  df-an 400  df-3an 1090  df-tru 1545  df-ex 1787  df-sb 2075  df-clab 2717  df-cleq 2730  df-clel 2811  df-ne 2935  df-ral 3058  df-rab 3062  df-v 3400  df-dif 3846  df-in 3850  df-ss 3860  df-pw 4490  df-uni 4797  df-tr 5137  df-wun 10202
This theorem is referenced by:  wuncn  10670
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