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Theorem bnj213 34357
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 34164 . 2 pred(𝑋, 𝐴, 𝑅) = {𝑦𝐴𝑦𝑅𝑋}
21ssrab3 4080 1 pred(𝑋, 𝐴, 𝑅) ⊆ 𝐴
Colors of variables: wff setvar class
Syntax hints:  wss 3948   class class class wbr 5148   predc-bnj14 34163
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2702
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1543  df-ex 1781  df-sb 2067  df-clab 2709  df-cleq 2723  df-clel 2809  df-rab 3432  df-v 3475  df-in 3955  df-ss 3965  df-bnj14 34164
This theorem is referenced by:  bnj229  34359  bnj517  34360  bnj1128  34465  bnj1145  34468  bnj1137  34470  bnj1408  34511  bnj1417  34516  bnj1523  34546
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