ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  mpteq12i Unicode version

Theorem mpteq12i 3892
Description: An equality inference for the maps to notation. (Contributed by Scott Fenton, 27-Oct-2010.) (Revised by Mario Carneiro, 16-Dec-2013.)
Hypotheses
Ref Expression
mpteq12i.1  |-  A  =  C
mpteq12i.2  |-  B  =  D
Assertion
Ref Expression
mpteq12i  |-  ( x  e.  A  |->  B )  =  ( x  e.  C  |->  D )

Proof of Theorem mpteq12i
StepHypRef Expression
1 mpteq12i.1 . . . 4  |-  A  =  C
21a1i 9 . . 3  |-  ( T. 
->  A  =  C
)
3 mpteq12i.2 . . . 4  |-  B  =  D
43a1i 9 . . 3  |-  ( T. 
->  B  =  D
)
52, 4mpteq12dv 3886 . 2  |-  ( T. 
->  ( x  e.  A  |->  B )  =  ( x  e.  C  |->  D ) )
65trud 1294 1  |-  ( x  e.  A  |->  B )  =  ( x  e.  C  |->  D )
Colors of variables: wff set class
Syntax hints:    = wceq 1285   T. wtru 1286    |-> cmpt 3865
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-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-ral 2358  df-opab 3866  df-mpt 3867
This theorem is referenced by:  offres  5839
  Copyright terms: Public domain W3C validator