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Theorem inex3 38340
Description: Sufficient condition for the intersection relation to be a set. (Contributed by Peter Mazsa, 24-Nov-2019.)
Assertion
Ref Expression
inex3 ((𝐴𝑉𝐵𝑊) → (𝐴𝐵) ∈ V)

Proof of Theorem inex3
StepHypRef Expression
1 inex1g 5318 . 2 (𝐴𝑉 → (𝐴𝐵) ∈ V)
2 inex2g 5319 . 2 (𝐵𝑊 → (𝐴𝐵) ∈ V)
31, 2jaoi 857 1 ((𝐴𝑉𝐵𝑊) → (𝐴𝐵) ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 847  wcel 2107  Vcvv 3479  cin 3949
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707  ax-sep 5295
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1542  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-rab 3436  df-v 3481  df-in 3957
This theorem is referenced by: (None)
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