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Theorem bnj1293 28526
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  =  ( B  i^i  C
)
Assertion
Ref Expression
bnj1293  |-  A  C_  C

Proof of Theorem bnj1293
StepHypRef Expression
1 bnj1293.1 . 2  |-  A  =  ( B  i^i  C
)
2 inss2 3505 . 2  |-  ( B  i^i  C )  C_  C
31, 2eqsstri 3321 1  |-  A  C_  C
Colors of variables: wff set class
Syntax hints:    = wceq 1649    i^i cin 3262    C_ wss 3263
This theorem is referenced by:  bnj1253  28724  bnj1286  28726  bnj1280  28727  bnj1296  28728
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-v 2901  df-in 3270  df-ss 3277
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