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Theorem mptcnv 24076
 Description: The converse of a mapping function. (Contributed by Thierry Arnoux, 16-Jan-2017.)
Hypothesis
Ref Expression
mptcnv.1
Assertion
Ref Expression
mptcnv
Distinct variable groups:   ,,   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem mptcnv
StepHypRef Expression
1 cnvopab 5303 . . 3
2 mptcnv.1 . . . 4
32opabbidv 4296 . . 3
41, 3syl5eq 2486 . 2
5 df-mpt 4293 . . 3
65cnveqi 5076 . 2
7 df-mpt 4293 . 2
84, 6, 73eqtr4g 2499 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   wceq 1653   wcel 1727  copab 4290   cmpt 4291  ccnv 4906 This theorem is referenced by:  ballotlemrinv  24822 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-14 1731  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423  ax-sep 4355  ax-nul 4363  ax-pr 4432 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2291  df-mo 2292  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ne 2607  df-ral 2716  df-rex 2717  df-rab 2720  df-v 2964  df-dif 3309  df-un 3311  df-in 3313  df-ss 3320  df-nul 3614  df-if 3764  df-sn 3844  df-pr 3845  df-op 3847  df-br 4238  df-opab 4292  df-mpt 4293  df-xp 4913  df-rel 4914  df-cnv 4915
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