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Mirrors > Home > ILE Home > Th. List > dftpos2 | Unicode version |
Description: Alternate definition of tpos when has relational domain. (Contributed by Mario Carneiro, 10-Sep-2015.) |
Ref | Expression |
---|---|
dftpos2 | tpos |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dmtpos 6153 | . . 3 tpos | |
2 | 1 | reseq2d 4819 | . 2 tpos tpos tpos |
3 | reltpos 6147 | . . 3 tpos | |
4 | resdm 4858 | . . 3 tpos tpos tpos tpos | |
5 | 3, 4 | ax-mp 5 | . 2 tpos tpos tpos |
6 | df-tpos 6142 | . . . 4 tpos | |
7 | 6 | reseq1i 4815 | . . 3 tpos |
8 | resco 5043 | . . 3 | |
9 | ssun1 3239 | . . . . 5 | |
10 | resmpt 4867 | . . . . 5 | |
11 | 9, 10 | ax-mp 5 | . . . 4 |
12 | 11 | coeq2i 4699 | . . 3 |
13 | 7, 8, 12 | 3eqtri 2164 | . 2 tpos |
14 | 2, 5, 13 | 3eqtr3g 2195 | 1 tpos |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 cun 3069 wss 3071 c0 3363 csn 3527 cuni 3736 cmpt 3989 ccnv 4538 cdm 4539 cres 4541 ccom 4543 wrel 4544 tpos ctpos 6141 |
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-in1 603 ax-in2 604 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-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-nul 4054 ax-pow 4098 ax-pr 4131 ax-un 4355 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-fal 1337 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-ne 2309 df-ral 2421 df-rex 2422 df-rab 2425 df-v 2688 df-sbc 2910 df-dif 3073 df-un 3075 df-in 3077 df-ss 3084 df-nul 3364 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 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-fv 5131 df-tpos 6142 |
This theorem is referenced by: tposf12 6166 |
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