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Theorem bnj1213 28595
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1213.1  |-  A  C_  B
bnj1213.2  |-  ( th 
->  x  e.  A
)
Assertion
Ref Expression
bnj1213  |-  ( th 
->  x  e.  B
)

Proof of Theorem bnj1213
StepHypRef Expression
1 bnj1213.1 . 2  |-  A  C_  B
2 bnj1213.2 . 2  |-  ( th 
->  x  e.  A
)
31, 2sseldi 3264 1  |-  ( th 
->  x  e.  B
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1715    C_ wss 3238
This theorem is referenced by:  bnj1212  28596  bnj1173  28796  bnj1296  28815  bnj1408  28830  bnj1452  28846  bnj1523  28865
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1551  ax-5 1562  ax-17 1621  ax-9 1659  ax-8 1680  ax-6 1734  ax-7 1739  ax-11 1751  ax-12 1937  ax-ext 2347
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1324  df-ex 1547  df-nf 1550  df-sb 1654  df-clab 2353  df-cleq 2359  df-clel 2362  df-in 3245  df-ss 3252
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