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Theorem idssxp 5884
 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 5883 . 2 ( I ∩ (𝐴 × 𝐴)) = ( I ↾ 𝐴)
2 inss2 4156 . 2 ( I ∩ (𝐴 × 𝐴)) ⊆ (𝐴 × 𝐴)
31, 2eqsstrri 3950 1 ( I ↾ 𝐴) ⊆ (𝐴 × 𝐴)
 Colors of variables: wff setvar class Syntax hints:   ∩ cin 3880   ⊆ wss 3881   I cid 5425   × cxp 5518   ↾ cres 5522 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 2113  ax-9 2121  ax-10 2142  ax-11 2158  ax-12 2175  ax-ext 2770  ax-sep 5168  ax-nul 5175  ax-pr 5296 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-mo 2598  df-eu 2629  df-clab 2777  df-cleq 2791  df-clel 2870  df-nfc 2938  df-ral 3111  df-rex 3112  df-rab 3115  df-v 3443  df-dif 3884  df-un 3886  df-in 3888  df-ss 3898  df-nul 4244  df-if 4426  df-sn 4526  df-pr 4528  df-op 4532  df-br 5032  df-opab 5094  df-id 5426  df-xp 5526  df-rel 5527  df-res 5532 This theorem is referenced by:  resiexg  7604  hartogslem1  8993  dfle2  12531  hausdiag  22260  qtophaus  31204  bj-imdirid  34620  bj-iminvid  34629  idresssidinxp  35745  rtrclex  40360  rtrclexi  40364  idhe  40531
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