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Theorem bnj213 29230
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj213  |-  pred ( X ,  A ,  R )  C_  A

Proof of Theorem bnj213
Dummy variable  y is distinct from all other variables.
StepHypRef Expression
1 df-bnj14 29030 . 2  |-  pred ( X ,  A ,  R )  =  {
y  e.  A  | 
y R X }
21bnj21 29059 1  |-  pred ( X ,  A ,  R )  C_  A
Colors of variables: wff set class
Syntax hints:    C_ wss 3165   class class class wbr 4039    predc-bnj14 29029
This theorem is referenced by:  bnj229  29232  bnj517  29233  bnj1128  29336  bnj1145  29339  bnj1137  29341  bnj1408  29382  bnj1417  29387  bnj1523  29417
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rab 2565  df-in 3172  df-ss 3179  df-bnj14 29030
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