Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  bdinex2 GIF version

Theorem bdinex2 13935
Description: Bounded version of inex2 4124. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bdinex2.bd BOUNDED 𝐵
bdinex2.1 𝐴 ∈ V
Assertion
Ref Expression
bdinex2 (𝐵𝐴) ∈ V

Proof of Theorem bdinex2
StepHypRef Expression
1 incom 3319 . 2 (𝐵𝐴) = (𝐴𝐵)
2 bdinex2.bd . . 3 BOUNDED 𝐵
3 bdinex2.1 . . 3 𝐴 ∈ V
42, 3bdinex1 13934 . 2 (𝐴𝐵) ∈ V
51, 4eqeltri 2243 1 (𝐵𝐴) ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 2141  Vcvv 2730  cin 3120  BOUNDED wbdc 13875
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152  ax-bdsep 13919
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-in 3127  df-bdc 13876
This theorem is referenced by:  bdssex  13937
  Copyright terms: Public domain W3C validator