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Theorem bnj213 33722
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 33529 . 2 pred(𝑋, 𝐴, 𝑅) = {𝑦𝐴𝑦𝑅𝑋}
21ssrab3 4076 1 pred(𝑋, 𝐴, 𝑅) ⊆ 𝐴
Colors of variables: wff setvar class
Syntax hints:  wss 3944   class class class wbr 5141   predc-bnj14 33528
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2702
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2709  df-cleq 2723  df-clel 2809  df-rab 3432  df-v 3475  df-in 3951  df-ss 3961  df-bnj14 33529
This theorem is referenced by:  bnj229  33724  bnj517  33725  bnj1128  33830  bnj1145  33833  bnj1137  33835  bnj1408  33876  bnj1417  33881  bnj1523  33911
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