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Theorem bnj213 28914
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 28714 . 2  |-  pred ( X ,  A ,  R )  =  {
y  e.  A  | 
y R X }
21bnj21 28743 1  |-  pred ( X ,  A ,  R )  C_  A
Colors of variables: wff set class
Syntax hints:    C_ wss 3152   class class class wbr 4023    predc-bnj14 28713
This theorem is referenced by:  bnj229  28916  bnj517  28917  bnj1128  29020  bnj1145  29023  bnj1137  29025  bnj1408  29066  bnj1417  29071  bnj1523  29101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rab 2552  df-in 3159  df-ss 3166  df-bnj14 28714
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