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Theorem inex2g 5320
Description: Sufficient condition for an intersection to be a set. Commuted form of inex1g 5319. (Contributed by Peter Mazsa, 19-Dec-2018.)
Assertion
Ref Expression
inex2g (𝐴𝑉 → (𝐵𝐴) ∈ V)

Proof of Theorem inex2g
StepHypRef Expression
1 incom 4201 . 2 (𝐵𝐴) = (𝐴𝐵)
2 inex1g 5319 . 2 (𝐴𝑉 → (𝐴𝐵) ∈ V)
31, 2eqeltrid 2833 1 (𝐴𝑉 → (𝐵𝐴) ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2099  Vcvv 3471  cin 3946
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2699  ax-sep 5299
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-rab 3430  df-v 3473  df-in 3954
This theorem is referenced by:  satefvfmla1  35035  inex3  37810  inxpex  37811  dfcnvrefrels2  38000  dfcnvrefrels3  38001  iunrelexp0  43132
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