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Theorem bnj21 29180
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj21.1  |-  B  =  { x  e.  A  |  ph }
Assertion
Ref Expression
bnj21  |-  B  C_  A
Distinct variable group:    x, A
Allowed substitution hints:    ph( x)    B( x)

Proof of Theorem bnj21
StepHypRef Expression
1 bnj21.1 . 2  |-  B  =  { x  e.  A  |  ph }
2 ssrab2 3414 . 2  |-  { x  e.  A  |  ph }  C_  A
31, 2eqsstri 3364 1  |-  B  C_  A
Colors of variables: wff set class
Syntax hints:    = wceq 1653   {crab 2715    C_ wss 3306
This theorem is referenced by:  bnj1212  29269  bnj213  29351  bnj1286  29486  bnj1312  29525  bnj1523  29538
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 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-rab 2720  df-in 3313  df-ss 3320
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