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Theorem bnj931 31169
 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 3919 . 2 𝐵 ⊆ (𝐵𝐶)
2 bnj931.1 . 2 𝐴 = (𝐵𝐶)
31, 2sseqtr4i 3779 1 𝐵𝐴
 Colors of variables: wff setvar class Syntax hints:   = wceq 1632   ∪ cun 3713   ⊆ wss 3715 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-clab 2747  df-cleq 2753  df-clel 2756  df-nfc 2891  df-v 3342  df-un 3720  df-in 3722  df-ss 3729 This theorem is referenced by:  bnj945  31172  bnj545  31293  bnj548  31295  bnj570  31303  bnj929  31334  bnj1136  31393  bnj1408  31432  bnj1442  31445
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