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Theorem bnj213 30206
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 30008 . 2 pred(𝑋, 𝐴, 𝑅) = {𝑦𝐴𝑦𝑅𝑋}
21bnj21 30037 1 pred(𝑋, 𝐴, 𝑅) ⊆ 𝐴
Colors of variables: wff setvar class
Syntax hints:  wss 3540   class class class wbr 4583   predc-bnj14 30007
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590
This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-rab 2905  df-in 3547  df-ss 3554  df-bnj14 30008
This theorem is referenced by:  bnj229  30208  bnj517  30209  bnj1128  30312  bnj1145  30315  bnj1137  30317  bnj1408  30358  bnj1417  30363  bnj1523  30393
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