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Theorem idssxp 6048
Description: A diagonal set as a subset of a Cartesian square. (Contributed by Thierry Arnoux, 29-Dec-2019.) (Proof shortened by BJ, 9-Sep-2022.)
Assertion
Ref Expression
idssxp ( I ↾ 𝐴) ⊆ (𝐴 × 𝐴)

Proof of Theorem idssxp
StepHypRef Expression
1 idinxpresid 6047 . 2 ( I ∩ (𝐴 × 𝐴)) = ( I ↾ 𝐴)
2 inss2 4229 . 2 ( I ∩ (𝐴 × 𝐴)) ⊆ (𝐴 × 𝐴)
31, 2eqsstrri 4017 1 ( I ↾ 𝐴) ⊆ (𝐴 × 𝐴)
Colors of variables: wff setvar class
Syntax hints:  cin 3947  wss 3948   I cid 5573   × cxp 5674  cres 5678
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 2703  ax-sep 5299  ax-nul 5306  ax-pr 5427
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-ral 3062  df-rex 3071  df-rab 3433  df-v 3476  df-dif 3951  df-un 3953  df-in 3955  df-ss 3965  df-nul 4323  df-if 4529  df-sn 4629  df-pr 4631  df-op 4635  df-br 5149  df-opab 5211  df-id 5574  df-xp 5682  df-rel 5683  df-res 5688
This theorem is referenced by:  resiexg  7904  hartogslem1  9536  dfle2  13125  hausdiag  23148  qtophaus  32811  bj-imdirid  36062  bj-iminvid  36071  idresssidinxp  37172  rtrclex  42358  rtrclexi  42362  idhe  42528
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