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Theorem bnj1213 29244
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 3348 1  |-  ( th 
->  x  e.  B
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1726    C_ wss 3322
This theorem is referenced by:  bnj1212  29245  bnj1173  29445  bnj1296  29464  bnj1408  29479  bnj1452  29495  bnj1523  29514
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-in 3329  df-ss 3336
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