Mathbox for Jonathan Ben-Naim < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj213 Structured version   Visualization version   GIF version

Theorem bnj213 31259
 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 31064 . 2 pred(𝑋, 𝐴, 𝑅) = {𝑦𝐴𝑦𝑅𝑋}
21ssrab3 3829 1 pred(𝑋, 𝐴, 𝑅) ⊆ 𝐴
 Colors of variables: wff setvar class Syntax hints:   ⊆ wss 3715   class class class wbr 4804   predc-bnj14 31063 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-clab 2747  df-cleq 2753  df-clel 2756  df-nfc 2891  df-rab 3059  df-in 3722  df-ss 3729  df-bnj14 31064 This theorem is referenced by:  bnj229  31261  bnj517  31262  bnj1128  31365  bnj1145  31368  bnj1137  31370  bnj1408  31411  bnj1417  31416  bnj1523  31446
 Copyright terms: Public domain W3C validator