Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > reltpos | Structured version Visualization version Unicode version |
Description: The transposition is a relation. (Contributed by Mario Carneiro, 10-Sep-2015.) |
Ref | Expression |
---|---|
reltpos | tpos |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tposssxp 7356 | . 2 tpos | |
2 | relxp 5227 | . 2 | |
3 | relss 5206 | . 2 tpos tpos | |
4 | 1, 2, 3 | mp2 9 | 1 tpos |
Colors of variables: wff setvar class |
Syntax hints: cun 3572 wss 3574 c0 3915 csn 4177 cxp 5112 ccnv 5113 cdm 5114 crn 5115 wrel 5119 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-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
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-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-opab 4713 df-mpt 4730 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-tpos 7352 |
This theorem is referenced by: brtpos2 7358 relbrtpos 7363 dftpos2 7369 dftpos3 7370 tpostpos 7372 |
Copyright terms: Public domain | W3C validator |