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Theorem mpt2mpts 6415
 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:   ,,,   ,,   ,   ,
Allowed substitution hints:   (,)

Proof of Theorem mpt2mpts
StepHypRef Expression
1 mpt2mptsx 6414 . 2
2 iunxpconst 4934 . . 3
3 mpteq1 4289 . . 3
42, 3ax-mp 8 . 2
51, 4eqtri 2456 1
 Colors of variables: wff set class Syntax hints:   wceq 1652  csb 3251  csn 3814  ciun 4093   cmpt 4266   cxp 4876  cfv 5454   cmpt2 6083  c1st 6347  c2nd 6348 This theorem is referenced by:  dfmpt2  6437 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-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pow 4377  ax-pr 4403  ax-un 4701 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 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-sbc 3162  df-csb 3252  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-iun 4095  df-br 4213  df-opab 4267  df-mpt 4268  df-id 4498  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-rn 4889  df-iota 5418  df-fun 5456  df-fv 5462  df-oprab 6085  df-mpt2 6086  df-1st 6349  df-2nd 6350
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