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Theorem mpt2mpt 5627
 Description: Express a two-argument function as a one-argument function, or vice-versa. (Contributed by Mario Carneiro, 17-Dec-2013.) (Revised by Mario Carneiro, 29-Dec-2014.)
Hypothesis
Ref Expression
mpt2mpt.1
Assertion
Ref Expression
mpt2mpt
Distinct variable groups:   ,,,   ,,   ,,   ,   ,
Allowed substitution hints:   ()   (,)

Proof of Theorem mpt2mpt
StepHypRef Expression
1 iunxpconst 4426 . . 3
2 mpteq1 3870 . . 3
31, 2ax-mp 7 . 2
4 mpt2mpt.1 . . 3
54mpt2mptx 5626 . 2
63, 5eqtr3i 2104 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1285  csn 3406  cop 3409  ciun 3686   cmpt 3847   cxp 4369   cmpt2 5545 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-sep 3904  ax-pow 3956  ax-pr 3972 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-rex 2355  df-v 2604  df-sbc 2817  df-csb 2910  df-un 2978  df-in 2980  df-ss 2987  df-pw 3392  df-sn 3412  df-pr 3413  df-op 3415  df-iun 3688  df-opab 3848  df-mpt 3849  df-xp 4377  df-rel 4378  df-oprab 5547  df-mpt2 5548 This theorem is referenced by:  fnovim  5640  fmpt2co  5868  xpf1o  6385
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