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Theorem tposfun 6963
 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 5617 . . 3
2 funco 5619 . . 3
31, 2mpan2 671 . 2
4 df-tpos 6947 . . 3 tpos
54funeqi 5601 . 2 tpos
63, 5sylibr 212 1 tpos
 Colors of variables: wff setvar class Syntax hints:   wi 4   cun 3469  c0 3780  csn 4022  cuni 4240   cmpt 4500  ccnv 4993   cdm 4994   ccom 4998   wfun 5575  tpos ctpos 6946 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-9 1766  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1963  ax-ext 2440  ax-sep 4563  ax-nul 4571  ax-pr 4681 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 970  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-eu 2274  df-mo 2275  df-clab 2448  df-cleq 2454  df-clel 2457  df-nfc 2612  df-ne 2659  df-ral 2814  df-rex 2815  df-rab 2818  df-v 3110  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-nul 3781  df-if 3935  df-sn 4023  df-pr 4025  df-op 4029  df-br 4443  df-opab 4501  df-mpt 4502  df-id 4790  df-xp 5000  df-rel 5001  df-cnv 5002  df-co 5003  df-fun 5583  df-tpos 6947 This theorem is referenced by:  tposfn2  6969
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