Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  tposfun Structured version   Unicode version

Theorem tposfun 6487
 Description: The transposition of a function is a function. (Contributed by Mario Carneiro, 10-Sep-2015.)
Assertion
Ref Expression
tposfun tpos

Proof of Theorem tposfun
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 funmpt 5481 . . 3
2 funco 5483 . . 3
31, 2mpan2 653 . 2
4 df-tpos 6471 . . 3 tpos
54funeqi 5466 . 2 tpos
63, 5sylibr 204 1 tpos
 Colors of variables: wff set class Syntax hints:   wi 4   cun 3310  c0 3620  csn 3806  cuni 4007   cmpt 4258  ccnv 4869   cdm 4870   ccom 4874   wfun 5440  tpos ctpos 6470 This theorem is referenced by:  tposfn2  6493 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-br 4205  df-opab 4259  df-mpt 4260  df-id 4490  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-fun 5448  df-tpos 6471
 Copyright terms: Public domain W3C validator