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Theorem bnj1293 31974
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1293.1 𝐴 = (𝐵𝐶)
Assertion
Ref Expression
bnj1293 𝐴𝐶

Proof of Theorem bnj1293
StepHypRef Expression
1 bnj1293.1 . 2 𝐴 = (𝐵𝐶)
2 inss2 4210 . 2 (𝐵𝐶) ⊆ 𝐶
31, 2eqsstri 4005 1 𝐴𝐶
 Colors of variables: wff setvar class Syntax hints:   = wceq 1530   ∩ cin 3939   ⊆ wss 3940 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 2798 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 2805  df-cleq 2819  df-clel 2898  df-nfc 2968  df-rab 3152  df-v 3502  df-in 3947  df-ss 3956 This theorem is referenced by:  bnj1253  32173  bnj1286  32175  bnj1280  32176  bnj1296  32177
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