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Mirrors > Home > MPE Home > Th. List > dftpos3 | Structured version Visualization version Unicode version |
Description: Alternate definition of tpos when has relational domain. Compare df-cnv 5122. (Contributed by Mario Carneiro, 10-Sep-2015.) |
Ref | Expression |
---|---|
dftpos3 | tpos |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | relcnv 5503 | . . . . . . . . . 10 | |
2 | dmtpos 7364 | . . . . . . . . . . 11 tpos | |
3 | 2 | releqd 5203 | . . . . . . . . . 10 tpos |
4 | 1, 3 | mpbiri 248 | . . . . . . . . 9 tpos |
5 | reltpos 7357 | . . . . . . . . 9 tpos | |
6 | 4, 5 | jctil 560 | . . . . . . . 8 tpos tpos |
7 | relrelss 5659 | . . . . . . . 8 tpos tpos tpos | |
8 | 6, 7 | sylib 208 | . . . . . . 7 tpos |
9 | 8 | sseld 3602 | . . . . . 6 tpos |
10 | elvvv 5178 | . . . . . 6 | |
11 | 9, 10 | syl6ib 241 | . . . . 5 tpos |
12 | 11 | pm4.71rd 667 | . . . 4 tpos tpos |
13 | 19.41vvv 1916 | . . . . 5 tpos tpos | |
14 | eleq1 2689 | . . . . . . . 8 tpos tpos | |
15 | df-br 4654 | . . . . . . . . 9 tpos tpos | |
16 | vex 3203 | . . . . . . . . . 10 | |
17 | brtpos 7361 | . . . . . . . . . 10 tpos | |
18 | 16, 17 | ax-mp 5 | . . . . . . . . 9 tpos |
19 | 15, 18 | bitr3i 266 | . . . . . . . 8 tpos |
20 | 14, 19 | syl6bb 276 | . . . . . . 7 tpos |
21 | 20 | pm5.32i 669 | . . . . . 6 tpos |
22 | 21 | 3exbii 1776 | . . . . 5 tpos |
23 | 13, 22 | bitr3i 266 | . . . 4 tpos |
24 | 12, 23 | syl6bb 276 | . . 3 tpos |
25 | 24 | abbi2dv 2742 | . 2 tpos |
26 | df-oprab 6654 | . 2 | |
27 | 25, 26 | syl6eqr 2674 | 1 tpos |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wex 1704 wcel 1990 cab 2608 cvv 3200 wss 3574 cop 4183 class class class wbr 4653 cxp 5112 ccnv 5113 cdm 5114 wrel 5119 coprab 6651 tpos ctpos 7351 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 ax-un 6949 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-fv 5896 df-oprab 6654 df-tpos 7352 |
This theorem is referenced by: tposoprab 7388 |
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