Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj931 Structured version   Visualization version   GIF version

Theorem bnj931 33596
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj931.1 𝐴 = (𝐵𝐶)
Assertion
Ref Expression
bnj931 𝐵𝐴

Proof of Theorem bnj931
StepHypRef Expression
1 ssun1 4165 . 2 𝐵 ⊆ (𝐵𝐶)
2 bnj931.1 . 2 𝐴 = (𝐵𝐶)
31, 2sseqtrri 4012 1 𝐵𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1541  cun 3939  wss 3941
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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2702
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2709  df-cleq 2723  df-clel 2809  df-v 3472  df-un 3946  df-in 3948  df-ss 3958
This theorem is referenced by:  bnj945  33599  bnj545  33721  bnj548  33723  bnj570  33731  bnj929  33762  bnj1136  33823  bnj1408  33862  bnj1442  33875
  Copyright terms: Public domain W3C validator