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

Theorem mptun 5057
 Description: Union of mappings which are mutually compatible. (Contributed by Mario Carneiro, 31-Aug-2015.)
Assertion
Ref Expression
mptun

Proof of Theorem mptun
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-mpt 3848 . 2
2 df-mpt 3848 . . . 4
3 df-mpt 3848 . . . 4
42, 3uneq12i 3123 . . 3
5 elun 3112 . . . . . . 7
65anbi1i 439 . . . . . 6
7 andir 743 . . . . . 6
86, 7bitri 177 . . . . 5
98opabbii 3852 . . . 4
10 unopab 3864 . . . 4
119, 10eqtr4i 2079 . . 3
124, 11eqtr4i 2079 . 2
131, 12eqtr4i 2079 1
 Colors of variables: wff set class Syntax hints:   wa 101   wo 639   wceq 1259   wcel 1409   cun 2943  copab 3845   cmpt 3846 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-un 2950  df-opab 3847  df-mpt 3848 This theorem is referenced by:  fmptap  5381  fmptapd  5382
 Copyright terms: Public domain W3C validator