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Theorem bnj1293 29934
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 3795 . 2 (𝐵𝐶) ⊆ 𝐶
31, 2eqsstri 3597 1 𝐴𝐶
Colors of variables: wff setvar class
Syntax hints:   = wceq 1474  cin 3538  wss 3539
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-10 2005  ax-11 2020  ax-12 2033  ax-13 2233  ax-ext 2589
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1867  df-clab 2596  df-cleq 2602  df-clel 2605  df-nfc 2739  df-v 3174  df-in 3546  df-ss 3553
This theorem is referenced by:  bnj1253  30132  bnj1286  30134  bnj1280  30135  bnj1296  30136
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