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Theorem bnj931 31351
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 3973 . 2 𝐵 ⊆ (𝐵𝐶)
2 bnj931.1 . 2 𝐴 = (𝐵𝐶)
31, 2sseqtr4i 3833 1 𝐵𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1653  cun 3766  wss 3768
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-9 2166  ax-10 2185  ax-11 2200  ax-12 2213  ax-ext 2776
This theorem depends on definitions:  df-bi 199  df-an 386  df-or 875  df-tru 1657  df-ex 1876  df-nf 1880  df-sb 2065  df-clab 2785  df-cleq 2791  df-clel 2794  df-nfc 2929  df-v 3386  df-un 3773  df-in 3775  df-ss 3782
This theorem is referenced by:  bnj945  31354  bnj545  31475  bnj548  31477  bnj570  31485  bnj929  31516  bnj1136  31575  bnj1408  31614  bnj1442  31627
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