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Theorem inex3 35127
 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 5114 . 2 (𝐴𝑉 → (𝐴𝐵) ∈ V)
2 inex2g 5115 . 2 (𝐵𝑊 → (𝐴𝐵) ∈ V)
31, 2jaoi 852 1 ((𝐴𝑉𝐵𝑊) → (𝐴𝐵) ∈ V)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∨ wo 842   ∈ wcel 2081  Vcvv 3437   ∩ cin 3858 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1777  ax-4 1791  ax-5 1888  ax-6 1947  ax-7 1992  ax-8 2083  ax-9 2091  ax-10 2112  ax-11 2126  ax-12 2141  ax-ext 2769  ax-sep 5094 This theorem depends on definitions:  df-bi 208  df-an 397  df-or 843  df-tru 1525  df-ex 1762  df-nf 1766  df-sb 2043  df-clab 2776  df-cleq 2788  df-clel 2863  df-nfc 2935  df-rab 3114  df-v 3439  df-in 3866 This theorem is referenced by: (None)
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