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Theorem bnj1293 29165
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 3403 . 2  |-  ( B  i^i  C )  C_  C
31, 2eqsstri 3221 1  |-  A  C_  C
Colors of variables: wff set class
Syntax hints:    = wceq 1632    i^i cin 3164    C_ wss 3165
This theorem is referenced by:  bnj1253  29363  bnj1286  29365  bnj1280  29366  bnj1296  29367
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-in 3172  df-ss 3179
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