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Theorem idssxp 6049
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 6048 . 2 ( I ∩ (𝐴 × 𝐴)) = ( I ↾ 𝐴)
2 inss2 4230 . 2 ( I ∩ (𝐴 × 𝐴)) ⊆ (𝐴 × 𝐴)
31, 2eqsstrri 4018 1 ( I ↾ 𝐴) ⊆ (𝐴 × 𝐴)
Colors of variables: wff setvar class
Syntax hints:  cin 3948  wss 3949   I cid 5574   × cxp 5675  cres 5679
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704  ax-sep 5300  ax-nul 5307  ax-pr 5428
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-ral 3063  df-rex 3072  df-rab 3434  df-v 3477  df-dif 3952  df-un 3954  df-in 3956  df-ss 3966  df-nul 4324  df-if 4530  df-sn 4630  df-pr 4632  df-op 4636  df-br 5150  df-opab 5212  df-id 5575  df-xp 5683  df-rel 5684  df-res 5689
This theorem is referenced by:  resiexg  7905  hartogslem1  9537  dfle2  13126  hausdiag  23149  qtophaus  32816  bj-imdirid  36067  bj-iminvid  36076  idresssidinxp  37177  rtrclex  42368  rtrclexi  42372  idhe  42538
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