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Theorem pssexg 40992
Description: The proper subset of a set is also a set. (Contributed by Steven Nguyen, 17-Jul-2022.)
Assertion
Ref Expression
pssexg ((𝐴𝐵𝐵𝐶) → 𝐴 ∈ V)

Proof of Theorem pssexg
StepHypRef Expression
1 pssss 4094 . 2 (𝐴𝐵𝐴𝐵)
2 ssexg 5322 . 2 ((𝐴𝐵𝐵𝐶) → 𝐴 ∈ V)
31, 2sylan 581 1 ((𝐴𝐵𝐵𝐶) → 𝐴 ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 397  wcel 2107  Vcvv 3475  wss 3947  wpss 3948
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704  ax-sep 5298
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-rab 3434  df-v 3477  df-in 3954  df-ss 3964  df-pss 3966
This theorem is referenced by: (None)
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