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Theorem bnj931 33512
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 4159 . 2 𝐵 ⊆ (𝐵𝐶)
2 bnj931.1 . 2 𝐴 = (𝐵𝐶)
31, 2sseqtrri 4006 1 𝐵𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1541  cun 3933  wss 3935
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 3468  df-un 3940  df-in 3942  df-ss 3952
This theorem is referenced by:  bnj945  33515  bnj545  33637  bnj548  33639  bnj570  33647  bnj929  33678  bnj1136  33739  bnj1408  33778  bnj1442  33791
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