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Theorem mpt20 5718
 Description: A mapping operation with empty domain. (Contributed by Stefan O'Rear, 29-Jan-2015.) (Revised by Mario Carneiro, 15-May-2015.)
Assertion
Ref Expression
mpt20

Proof of Theorem mpt20
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-mpt2 5657 . 2
2 df-oprab 5656 . 2
3 noel 3290 . . . . . . 7
4 simprll 504 . . . . . . 7
53, 4mto 623 . . . . . 6
65nex 1434 . . . . 5
76nex 1434 . . . 4
87nex 1434 . . 3
98abf 3326 . 2
101, 2, 93eqtri 2112 1
 Colors of variables: wff set class Syntax hints:   wa 102   wceq 1289  wex 1426   wcel 1438  cab 2074  c0 3286  cop 3449  coprab 5653   cmpt2 5654 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-in1 579  ax-in2 580  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070 This theorem depends on definitions:  df-bi 115  df-tru 1292  df-fal 1295  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-dif 3001  df-in 3005  df-ss 3012  df-nul 3287  df-oprab 5656  df-mpt2 5657 This theorem is referenced by: (None)
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