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Theorem pssexg 39426
 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 4023 . 2 (𝐴𝐵𝐴𝐵)
2 ssexg 5192 . 2 ((𝐴𝐵𝐵𝐶) → 𝐴 ∈ V)
31, 2sylan 583 1 ((𝐴𝐵𝐵𝐶) → 𝐴 ∈ V)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 399   ∈ wcel 2111  Vcvv 3441   ⊆ wss 3881   ⊊ wpss 3882 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-ext 2770  ax-sep 5168 This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1541  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-rab 3115  df-v 3443  df-in 3888  df-ss 3898  df-pss 3900 This theorem is referenced by: (None)
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