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Theorem inex2g 5281
Description: Sufficient condition for an intersection to be a set. Commuted form of inex1g 5280. (Contributed by Peter Mazsa, 19-Dec-2018.)
Assertion
Ref Expression
inex2g (𝐴𝑉 → (𝐵𝐴) ∈ V)

Proof of Theorem inex2g
StepHypRef Expression
1 incom 4165 . 2 (𝐵𝐴) = (𝐴𝐵)
2 inex1g 5280 . 2 (𝐴𝑉 → (𝐴𝐵) ∈ V)
31, 2eqeltrid 2838 1 (𝐴𝑉 → (𝐵𝐴) ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2107  Vcvv 3447  cin 3913
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 5260
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 3407  df-v 3449  df-in 3921
This theorem is referenced by:  satefvfmla1  34083  inex3  36849  inxpex  36850  dfcnvrefrels2  37040  dfcnvrefrels3  37041  iunrelexp0  42066
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