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Theorem inex2ALTV 35069
 Description: Sufficient condition for an intersection relation to be a set, see also inex1g 5076. (Contributed by Peter Mazsa, 19-Dec-2018.)
Assertion
Ref Expression
inex2ALTV (𝐴𝑉 → (𝐵𝐴) ∈ V)

Proof of Theorem inex2ALTV
StepHypRef Expression
1 incom 4060 . 2 (𝐵𝐴) = (𝐴𝐵)
2 inex1g 5076 . 2 (𝐴𝑉 → (𝐴𝐵) ∈ V)
31, 2syl5eqel 2864 1 (𝐴𝑉 → (𝐵𝐴) ∈ V)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 2050  Vcvv 3409   ∩ cin 3822 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1965  ax-8 2052  ax-9 2059  ax-10 2079  ax-11 2093  ax-12 2106  ax-ext 2744  ax-sep 5056 This theorem depends on definitions:  df-bi 199  df-an 388  df-or 834  df-tru 1510  df-ex 1743  df-nf 1747  df-sb 2016  df-clab 2753  df-cleq 2765  df-clel 2840  df-nfc 2912  df-rab 3091  df-v 3411  df-in 3830 This theorem is referenced by:  inex3  35070  inxpex  35071  dfcnvrefrels2  35240  dfcnvrefrels3  35241
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