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Theorem xpcoid 5553
 Description: Composition of two square Cartesian products. (Contributed by Thierry Arnoux, 14-Jan-2018.)
Assertion
Ref Expression
xpcoid

Proof of Theorem xpcoid
StepHypRef Expression
1 co01 5527 . . 3
2 id 22 . . . . . 6
32sqxpeqd 5030 . . . . 5
4 0xp 5085 . . . . 5
53, 4syl6eq 2514 . . . 4
65, 5coeq12d 5172 . . 3
71, 6, 53eqtr4a 2524 . 2
8 xpco 5552 . 2
97, 8pm2.61ine 2770 1
 Colors of variables: wff setvar class Syntax hints:  =wceq 1395   c0 3784  X.cxp 5002  o.ccom 5008 This theorem is referenced by:  utop2nei  20753 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013
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