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Mirrors > Home > ILE Home > Th. List > idref | Unicode version |
Description: TODO: This is the same
as issref 4921 (which has a much longer proof).
Should we replace issref 4921 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.) |
Ref | Expression |
---|---|
idref |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2139 | . . . 4 | |
2 | 1 | fmpt 5570 | . . 3 |
3 | vex 2689 | . . . . . 6 | |
4 | 3, 3 | opex 4151 | . . . . 5 |
5 | 4, 1 | fnmpti 5251 | . . . 4 |
6 | df-f 5127 | . . . 4 | |
7 | 5, 6 | mpbiran 924 | . . 3 |
8 | 2, 7 | bitri 183 | . 2 |
9 | df-br 3930 | . . 3 | |
10 | 9 | ralbii 2441 | . 2 |
11 | mptresid 4873 | . . . 4 | |
12 | 3 | fnasrn 5598 | . . . 4 |
13 | 11, 12 | eqtr3i 2162 | . . 3 |
14 | 13 | sseq1i 3123 | . 2 |
15 | 8, 10, 14 | 3bitr4ri 212 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wcel 1480 wral 2416 wss 3071 cop 3530 class class class wbr 3929 cmpt 3989 cid 4210 crn 4540 cres 4541 wfn 5118 wf 5119 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-reu 2423 df-rab 2425 df-v 2688 df-sbc 2910 df-csb 3004 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-iun 3815 df-br 3930 df-opab 3990 df-mpt 3991 df-id 4215 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-rn 4550 df-res 4551 df-ima 4552 df-iota 5088 df-fun 5125 df-fn 5126 df-f 5127 df-f1 5128 df-fo 5129 df-f1o 5130 df-fv 5131 |
This theorem is referenced by: (None) |
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