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Theorem isprsr 25224
 Description: The predicate "is a preset". (Contributed by FL, 1-May-2011.)
Assertion
Ref Expression
isprsr PresetRel

Proof of Theorem isprsr
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 releq 4771 . . 3
2 coeq1 4841 . . . . 5
3 coeq2 4842 . . . . 5
42, 3eqtrd 2315 . . . 4
5 sseq12 3201 . . . 4
64, 5mpancom 650 . . 3
7 unieq 3836 . . . . . 6
87unieqd 3838 . . . . 5
98reseq2d 4955 . . . 4
10 sseq12 3201 . . . 4
119, 10mpancom 650 . . 3
121, 6, 113anbi123d 1252 . 2
13 df-prs 25223 . 2 PresetRel
1412, 13elab2g 2916 1 PresetRel
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   w3a 934   wceq 1623   wcel 1684   wss 3152  cuni 3827   cid 4304   cres 4691   ccom 4693   wrel 4694  PresetRelcpresetrel 25215 This theorem is referenced by:  preorel  25225  preodom2  25226  preoref12  25228  preoran2  25230  preotr1  25234  altprs2  25236  int2pre  25237  sqpre  25238  dupre1  25243  dfdir2  25291 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rex 2549  df-v 2790  df-in 3159  df-ss 3166  df-uni 3828  df-br 4024  df-opab 4078  df-xp 4695  df-rel 4696  df-co 4698  df-res 4701  df-prs 25223
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