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Theorem inex2g 5326
Description: Sufficient condition for an intersection to be a set. Commuted form of inex1g 5325. (Contributed by Peter Mazsa, 19-Dec-2018.)
Assertion
Ref Expression
inex2g (𝐴𝑉 → (𝐵𝐴) ∈ V)

Proof of Theorem inex2g
StepHypRef Expression
1 incom 4217 . 2 (𝐵𝐴) = (𝐴𝐵)
2 inex1g 5325 . 2 (𝐴𝑉 → (𝐴𝐵) ∈ V)
31, 2eqeltrid 2843 1 (𝐴𝑉 → (𝐵𝐴) ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2106  Vcvv 3478  cin 3962
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706  ax-sep 5302
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-rab 3434  df-v 3480  df-in 3970
This theorem is referenced by:  satefvfmla1  35410  inex3  38320  inxpex  38321  dfcnvrefrels2  38510  dfcnvrefrels3  38511  iunrelexp0  43692
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