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Theorem bnj931 31930
 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 4151 . 2 𝐵 ⊆ (𝐵𝐶)
2 bnj931.1 . 2 𝐴 = (𝐵𝐶)
31, 2sseqtrri 4007 1 𝐵𝐴
 Colors of variables: wff setvar class Syntax hints:   = wceq 1530   ∪ cun 3937   ⊆ wss 3939 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2153  ax-12 2169  ax-ext 2797 This theorem depends on definitions:  df-bi 208  df-an 397  df-or 844  df-tru 1533  df-ex 1774  df-nf 1778  df-sb 2063  df-clab 2804  df-cleq 2818  df-clel 2897  df-nfc 2967  df-v 3501  df-un 3944  df-in 3946  df-ss 3955 This theorem is referenced by:  bnj945  31933  bnj545  32055  bnj548  32057  bnj570  32065  bnj929  32096  bnj1136  32155  bnj1408  32194  bnj1442  32207
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