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Theorem bnj213 32188
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 31990 . 2  |-  pred ( X ,  A ,  R )  =  {
y  e.  A  | 
y R X }
21bnj21 32019 1  |-  pred ( X ,  A ,  R )  C_  A
Colors of variables: wff setvar class
Syntax hints:    C_ wss 3431   class class class wbr 4395    predc-bnj14 31989
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1954  ax-ext 2431
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2602  df-rab 2805  df-in 3438  df-ss 3445  df-bnj14 31990
This theorem is referenced by:  bnj229  32190  bnj517  32191  bnj1128  32294  bnj1145  32297  bnj1137  32299  bnj1408  32340  bnj1417  32345  bnj1523  32375
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