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Theorem pwuninel2 8299
Description: Proof of pwuninel 8300 under the assumption that the union of the given class is a set, avoiding ax-pr 5432 and ax-un 7755. (Contributed by Stefan O'Rear, 22-Feb-2015.)
Assertion
Ref Expression
pwuninel2 ( 𝐴𝑉 → ¬ 𝒫 𝐴𝐴)

Proof of Theorem pwuninel2
StepHypRef Expression
1 pwnss 5352 . 2 ( 𝐴𝑉 → ¬ 𝒫 𝐴 𝐴)
2 elssuni 4937 . 2 (𝒫 𝐴𝐴 → 𝒫 𝐴 𝐴)
31, 2nsyl 140 1 ( 𝐴𝑉 → ¬ 𝒫 𝐴𝐴)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wcel 2108  wss 3951  𝒫 cpw 4600   cuni 4907
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708  ax-sep 5296
This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1089  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-rab 3437  df-v 3482  df-in 3958  df-ss 3968  df-pw 4602  df-uni 4908
This theorem is referenced by:  pwuninel  8300
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