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Theorem bnj1213 28880
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 3310 1  |-  ( th 
->  x  e.  B
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1721    C_ wss 3284
This theorem is referenced by:  bnj1212  28881  bnj1173  29081  bnj1296  29100  bnj1408  29115  bnj1452  29131  bnj1523  29150
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 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2389
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2395  df-cleq 2401  df-clel 2404  df-in 3291  df-ss 3298
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