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Theorem relssdmrn 5533
 Description: A relation is included in the Cartesian product of its domain and range. Exercise 4.12(t) of [Mendelson] p. 235. (Contributed by NM, 3-Aug-1994.)
Assertion
Ref Expression
relssdmrn

Proof of Theorem relssdmrn
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 id 22 . 2
2 19.8a 1857 . . . 4
3 19.8a 1857 . . . 4
4 opelxp 5034 . . . . 5
5 vex 3112 . . . . . . 7
65eldm2 5206 . . . . . 6
7 vex 3112 . . . . . . 7
87elrn2 5247 . . . . . 6
96, 8anbi12i 697 . . . . 5
104, 9bitri 249 . . . 4
112, 3, 10sylanbrc 664 . . 3
1211a1i 11 . 2
131, 12relssdv 5100 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  E.wex 1612  e.wcel 1818  C_wss 3475  <.cop 4035  X.cxp 5002  domcdm 5004  rancrn 5005  Relwrel 5009 This theorem is referenced by:  cnvssrndm  5534  cossxp  5535  relrelss  5536  relfld  5538  fssxp  5748  oprabss  6388  cnvexg  6746  resfunexgALT  6763  cofunexg  6764  fnexALT  6766  erssxp  7353  wunco  9132  imasless  14937  sylow2a  16639  gsum2d  16999  gsum2dOLD  17000  znleval  18593  tsmsxp  20657  relfi  27459  idssxp  27469  fcnvgreu  27514  trrelsuperreldg  37783  trclub  37784  trclubg  37785  rp-imass  37795  idhe  37810 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-dm 5014  df-rn 5015
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