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Theorem bnj21 29573
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 3526 . 2  |-  { x  e.  A  |  ph }  C_  A
31, 2eqsstri 3474 1  |-  B  C_  A
Colors of variables: wff setvar class
Syntax hints:    = wceq 1455   {crab 2753    C_ wss 3416
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1680  ax-4 1693  ax-5 1769  ax-6 1816  ax-7 1862  ax-10 1926  ax-11 1931  ax-12 1944  ax-13 2102  ax-ext 2442
This theorem depends on definitions:  df-bi 190  df-or 376  df-an 377  df-tru 1458  df-ex 1675  df-nf 1679  df-sb 1809  df-clab 2449  df-cleq 2455  df-clel 2458  df-nfc 2592  df-rab 2758  df-in 3423  df-ss 3430
This theorem is referenced by:  bnj1212  29661  bnj213  29743  bnj1286  29878  bnj1312  29917  bnj1523  29930
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