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Theorem pssexg 42265
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 4098 . 2 (𝐴𝐵𝐴𝐵)
2 ssexg 5323 . 2 ((𝐴𝐵𝐵𝐶) → 𝐴 ∈ V)
31, 2sylan 580 1 ((𝐴𝐵𝐵𝐶) → 𝐴 ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395  wcel 2108  Vcvv 3480  wss 3951  wpss 3952
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-pss 3971
This theorem is referenced by: (None)
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