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Theorem bnj1293 31215
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 4037 . 2 (𝐵𝐶) ⊆ 𝐶
31, 2eqsstri 3839 1 𝐴𝐶
Colors of variables: wff setvar class
Syntax hints:   = wceq 1637  cin 3775  wss 3776
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1877  ax-4 1894  ax-5 2001  ax-6 2069  ax-7 2105  ax-9 2166  ax-10 2186  ax-11 2202  ax-12 2215  ax-13 2422  ax-ext 2791
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 866  df-tru 1641  df-ex 1860  df-nf 1864  df-sb 2062  df-clab 2800  df-cleq 2806  df-clel 2809  df-nfc 2944  df-v 3400  df-in 3783  df-ss 3790
This theorem is referenced by:  bnj1253  31413  bnj1286  31415  bnj1280  31416  bnj1296  31417
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