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Theorem bnj1293 31987
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 4203 . 2 (𝐵𝐶) ⊆ 𝐶
31, 2eqsstri 3998 1 𝐴𝐶
Colors of variables: wff setvar class
Syntax hints:   = wceq 1528  cin 3932  wss 3933
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-nfc 2960  df-rab 3144  df-v 3494  df-in 3940  df-ss 3949
This theorem is referenced by:  bnj1253  32186  bnj1286  32188  bnj1280  32189  bnj1296  32190
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