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Theorem relssdmrn 4871
 Description: A relation is included in the cross 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 19 . 2
2 19.8a 1523 . . . 4
3 19.8a 1523 . . . 4
4 opelxp 4400 . . . . 5
5 vex 2605 . . . . . . 7
65eldm2 4561 . . . . . 6
7 vex 2605 . . . . . . 7
87elrn2 4604 . . . . . 6
96, 8anbi12i 448 . . . . 5
104, 9bitri 182 . . . 4
112, 3, 10sylanbrc 408 . . 3
1211a1i 9 . 2
131, 12relssdv 4458 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102  wex 1422   wcel 1434   wss 2974  cop 3409   cxp 4369   cdm 4371   crn 4372   wrel 4376 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-sep 3904  ax-pow 3956  ax-pr 3972 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-eu 1945  df-mo 1946  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-rex 2355  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-pw 3392  df-sn 3412  df-pr 3413  df-op 3415  df-br 3794  df-opab 3848  df-xp 4377  df-rel 4378  df-cnv 4379  df-dm 4381  df-rn 4382 This theorem is referenced by:  cnvssrndm  4872  cossxp  4873  relrelss  4874  relfld  4876  cnvexg  4885  fssxp  5089  oprabss  5621  resfunexgALT  5768  cofunexg  5769  fnexALT  5771  erssxp  6195
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