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Theorem bnj213 32228
 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 32033 . 2 pred(𝑋, 𝐴, 𝑅) = {𝑦𝐴𝑦𝑅𝑋}
21ssrab3 4032 1 pred(𝑋, 𝐴, 𝑅) ⊆ 𝐴
 Colors of variables: wff setvar class Syntax hints:   ⊆ wss 3908   class class class wbr 5042   predc-bnj14 32032 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 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2178  ax-ext 2794 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2801  df-cleq 2815  df-clel 2894  df-nfc 2962  df-rab 3139  df-v 3471  df-in 3915  df-ss 3925  df-bnj14 32033 This theorem is referenced by:  bnj229  32230  bnj517  32231  bnj1128  32336  bnj1145  32339  bnj1137  32341  bnj1408  32382  bnj1417  32387  bnj1523  32417
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