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Theorem bnj1292 31905
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1292.1  |-  A  =  ( B  i^i  C
)
Assertion
Ref Expression
bnj1292  |-  A  C_  B

Proof of Theorem bnj1292
StepHypRef Expression
1 bnj1292.1 . 2  |-  A  =  ( B  i^i  C
)
2 inss1 3591 . 2  |-  ( B  i^i  C )  C_  B
31, 2eqsstri 3407 1  |-  A  C_  B
Colors of variables: wff setvar class
Syntax hints:    = wceq 1369    i^i cin 3348    C_ wss 3349
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2577  df-v 2995  df-in 3356  df-ss 3363
This theorem is referenced by:  bnj1253  32104  bnj1286  32106  bnj1280  32107  bnj1296  32108
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