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Theorem idref 5422
 Description: TODO: This is the same as issref 4731 (which has a much longer proof). Should we replace issref 4731 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 2082 . . . 4
21fmpt 5345 . . 3
3 vex 2605 . . . . . 6
43, 3opex 3986 . . . . 5
54, 1fnmpti 5052 . . . 4
6 df-f 4930 . . . 4
75, 6mpbiran 882 . . 3
82, 7bitri 182 . 2
9 df-br 3788 . . 3
109ralbii 2373 . 2
11 mptresid 4684 . . . 4
123fnasrn 5367 . . . 4
1311, 12eqtr3i 2104 . . 3
1413sseq1i 3024 . 2
158, 10, 143bitr4ri 211 1
 Colors of variables: wff set class Syntax hints:   wb 103   wcel 1434  wral 2349   wss 2974  cop 3403   class class class wbr 3787   cmpt 3841   cid 4045   crn 4366   cres 4367   wfn 4921  wf 4922 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 3898  ax-pow 3950  ax-pr 3966 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-reu 2356  df-rab 2358  df-v 2604  df-sbc 2817  df-csb 2910  df-un 2978  df-in 2980  df-ss 2987  df-pw 3386  df-sn 3406  df-pr 3407  df-op 3409  df-uni 3604  df-iun 3682  df-br 3788  df-opab 3842  df-mpt 3843  df-id 4050  df-xp 4371  df-rel 4372  df-cnv 4373  df-co 4374  df-dm 4375  df-rn 4376  df-res 4377  df-ima 4378  df-iota 4891  df-fun 4928  df-fn 4929  df-f 4930  df-f1 4931  df-fo 4932  df-f1o 4933  df-fv 4934 This theorem is referenced by: (None)
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