MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  mpt2mpts Unicode version

Theorem mpt2mpts 6607
Description: Express a two-argument function as a one-argument function, or vice-versa. (Contributed by Mario Carneiro, 24-Sep-2015.)
Assertion
Ref Expression
mpt2mpts
Distinct variable groups:   , , ,   , ,   ,   ,

Proof of Theorem mpt2mpts
StepHypRef Expression
1 mpt2mptsx 6606 . 2
2 iunxpconst 4866 . . 3
3 mpteq1 4347 . . 3
42, 3ax-mp 5 . 2
51, 4eqtri 2442 1
Colors of variables: wff setvar class
Syntax hints:  =wceq 1687  [_csb 3265  {csn 3853  U_ciun 4146  e.cmpt 4325  X.cxp 4809  `cfv 5390  e.cmpt2 6063   c1st 6544   c2nd 6545
This theorem is referenced by:  offval22  6621  dfmpt2  6632
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1586  ax-4 1597  ax-5 1661  ax-6 1701  ax-7 1721  ax-8 1751  ax-9 1753  ax-10 1768  ax-11 1773  ax-12 1785  ax-13 1934  ax-ext 2403  ax-sep 4388  ax-nul 4396  ax-pow 4442  ax-pr 4503  ax-un 6342
This theorem depends on definitions:  df-bi 179  df-or 363  df-an 364  df-3an 952  df-tru 1355  df-ex 1582  df-nf 1585  df-sb 1694  df-eu 2248  df-mo 2249  df-clab 2409  df-cleq 2415  df-clel 2418  df-nfc 2547  df-ne 2587  df-ral 2699  df-rex 2700  df-rab 2703  df-v 2953  df-sbc 3165  df-csb 3266  df-dif 3308  df-un 3310  df-in 3312  df-ss 3319  df-nul 3615  df-if 3769  df-sn 3859  df-pr 3860  df-op 3862  df-uni 4067  df-iun 4148  df-br 4268  df-opab 4326  df-mpt 4327  df-id 4607  df-xp 4817  df-rel 4818  df-cnv 4819  df-co 4820  df-dm 4821  df-rn 4822  df-iota 5353  df-fun 5392  df-fv 5398  df-oprab 6065  df-mpt2 6066  df-1st 6546  df-2nd 6547
  Copyright terms: Public domain W3C validator