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Theorem bnj213 30937
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) ⊆ 𝐴

Proof of Theorem bnj213
Dummy variable 𝑦 is distinct from all other variables.
StepHypRef Expression
1 df-bnj14 30740 . 2 pred(𝑋, 𝐴, 𝑅) = {𝑦𝐴𝑦𝑅𝑋}
21ssrab3 3686 1 pred(𝑋, 𝐴, 𝑅) ⊆ 𝐴
Colors of variables: wff setvar class
Syntax hints:  wss 3572   class class class wbr 4651   predc-bnj14 30739
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1721  ax-4 1736  ax-5 1838  ax-6 1887  ax-7 1934  ax-9 1998  ax-10 2018  ax-11 2033  ax-12 2046  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1485  df-ex 1704  df-nf 1709  df-sb 1880  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2752  df-rab 2920  df-in 3579  df-ss 3586  df-bnj14 30740
This theorem is referenced by:  bnj229  30939  bnj517  30940  bnj1128  31043  bnj1145  31046  bnj1137  31048  bnj1408  31089  bnj1417  31094  bnj1523  31124
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