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Theorem idref 5759
 Description: TODO: This is the same as issref 5056 (which has a much longer proof). Should we replace issref 5056 with this one? - NM 9-May-2016. Two ways to state a relation is reflexive. (Adapted from Tarski.) (Contributed by FL, 15-Jan-2012.) (Proof shortened by Mario Carneiro, 3-Nov-2015.) (Proof modification is discouraged.)
Assertion
Ref Expression
idref
Distinct variable groups:   ,   ,

Proof of Theorem idref
StepHypRef Expression
1 eqid 2283 . . . 4
21fmpt 5681 . . 3
3 opex 4237 . . . . 5
43, 1fnmpti 5372 . . . 4
5 df-f 5259 . . . 4
64, 5mpbiran 884 . . 3
72, 6bitri 240 . 2
8 df-br 4024 . . 3
98ralbii 2567 . 2
10 mptresid 5004 . . . 4
11 vex 2791 . . . . 5
1211fnasrn 5702 . . . 4
1310, 12eqtr3i 2305 . . 3
1413sseq1i 3202 . 2
157, 9, 143bitr4ri 269 1
 Colors of variables: wff set class Syntax hints:   wb 176   wcel 1684  wral 2543   wss 3152  cop 3643   class class class wbr 4023   cmpt 4077   cid 4304   crn 4690   cres 4691   wfn 5250  wf 5251 This theorem is referenced by:  preoref22  25229  preoran2  25230  dfps2  25289  filnetlem2  26328 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-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214 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-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-reu 2550  df-rab 2552  df-v 2790  df-sbc 2992  df-csb 3082  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-iun 3907  df-br 4024  df-opab 4078  df-mpt 4079  df-id 4309  df-xp 4695  df-rel 4696  df-cnv 4697  df-co 4698  df-dm 4699  df-rn 4700  df-res 4701  df-ima 4702  df-iota 5219  df-fun 5257  df-fn 5258  df-f 5259  df-f1 5260  df-fo 5261  df-f1o 5262  df-fv 5263
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