Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  mpo0 Unicode version

Theorem mpo0 5807
 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
mpo0

Proof of Theorem mpo0
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-mpo 5745 . 2
2 df-oprab 5744 . 2
3 noel 3335 . . . . . . 7
4 simprll 509 . . . . . . 7
53, 4mto 634 . . . . . 6
65nex 1459 . . . . 5
76nex 1459 . . . 4
87nex 1459 . . 3
98abf 3374 . 2
101, 2, 93eqtri 2140 1
 Colors of variables: wff set class Syntax hints:   wa 103   wceq 1314  wex 1451   wcel 1463  cab 2101  c0 3331  cop 3498  coprab 5741   cmpo 5742 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-tru 1317  df-fal 1320  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-dif 3041  df-in 3045  df-ss 3052  df-nul 3332  df-oprab 5744  df-mpo 5745 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator