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Theorem inex2g 5200
 Description: Sufficient condition for an intersection to be a set. Commuted form of inex1g 5199. (Contributed by Peter Mazsa, 19-Dec-2018.)
Assertion
Ref Expression
inex2g (𝐴𝑉 → (𝐵𝐴) ∈ V)

Proof of Theorem inex2g
StepHypRef Expression
1 incom 4152 . 2 (𝐵𝐴) = (𝐴𝐵)
2 inex1g 5199 . 2 (𝐴𝑉 → (𝐴𝐵) ∈ V)
31, 2eqeltrid 2918 1 (𝐴𝑉 → (𝐵𝐴) ∈ V)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 2114  Vcvv 3469   ∩ cin 3907 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 2116  ax-9 2124  ax-ext 2794  ax-sep 5179 This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1541  df-ex 1782  df-sb 2070  df-clab 2801  df-cleq 2815  df-clel 2894  df-rab 3139  df-v 3471  df-in 3915 This theorem is referenced by:  satefvfmla1  32746  inex3  35713  inxpex  35714  dfcnvrefrels2  35884  dfcnvrefrels3  35885
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