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Theorem bnj213 33019
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 32821 . 2  |-  pred ( X ,  A ,  R )  =  {
y  e.  A  | 
y R X }
21bnj21 32850 1  |-  pred ( X ,  A ,  R )  C_  A
Colors of variables: wff setvar class
Syntax hints:    C_ wss 3476   class class class wbr 4447    predc-bnj14 32820
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-rab 2823  df-in 3483  df-ss 3490  df-bnj14 32821
This theorem is referenced by:  bnj229  33021  bnj517  33022  bnj1128  33125  bnj1145  33128  bnj1137  33130  bnj1408  33171  bnj1417  33176  bnj1523  33206
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