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Theorem idssxp 5916
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 5915 . 2 ( I ∩ (𝐴 × 𝐴)) = ( I ↾ 𝐴)
2 inss2 4144 . 2 ( I ∩ (𝐴 × 𝐴)) ⊆ (𝐴 × 𝐴)
31, 2eqsstrri 3936 1 ( I ↾ 𝐴) ⊆ (𝐴 × 𝐴)
Colors of variables: wff setvar class
Syntax hints:  cin 3865  wss 3866   I cid 5454   × cxp 5549  cres 5553
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2112  ax-9 2120  ax-ext 2708  ax-sep 5192  ax-nul 5199  ax-pr 5322
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 848  df-3an 1091  df-tru 1546  df-fal 1556  df-ex 1788  df-sb 2071  df-clab 2715  df-cleq 2729  df-clel 2816  df-ral 3066  df-rex 3067  df-rab 3070  df-v 3410  df-dif 3869  df-un 3871  df-in 3873  df-ss 3883  df-nul 4238  df-if 4440  df-sn 4542  df-pr 4544  df-op 4548  df-br 5054  df-opab 5116  df-id 5455  df-xp 5557  df-rel 5558  df-res 5563
This theorem is referenced by:  resiexg  7692  hartogslem1  9158  dfle2  12737  hausdiag  22542  qtophaus  31500  bj-imdirid  35092  bj-iminvid  35101  idresssidinxp  36181  rtrclex  40901  rtrclexi  40905  idhe  41072
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