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Theorem bnj213 34360
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 34161 . 2  |-  pred ( X ,  A ,  R )  =  {
y  e.  A  | 
y R X }
21bnj21 34190 1  |-  pred ( X ,  A ,  R )  C_  A
Colors of variables: wff setvar class
Syntax hints:    C_ wss 3461   class class class wbr 4439    predc-bnj14 34160
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-rab 2813  df-in 3468  df-ss 3475  df-bnj14 34161
This theorem is referenced by:  bnj229  34362  bnj517  34363  bnj1128  34466  bnj1145  34469  bnj1137  34471  bnj1408  34512  bnj1417  34517  bnj1523  34547
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