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Theorem mpteq12i 4508
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 11 . . 3  |-  ( T. 
->  A  =  C
)
3 mpteq12i.2 . . . 4  |-  B  =  D
43a1i 11 . . 3  |-  ( T. 
->  B  =  D
)
52, 4mpteq12dv 4502 . 2  |-  ( T. 
->  ( x  e.  A  |->  B )  =  ( x  e.  C  |->  D ) )
65trud 1446 1  |-  ( x  e.  A  |->  B )  =  ( x  e.  C  |->  D )
Colors of variables: wff setvar class
Syntax hints:    = wceq 1437   T. wtru 1438    |-> cmpt 4482
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401
This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-ral 2776  df-opab 4483  df-mpt 4484
This theorem is referenced by:  offres  6802  pmtrprfval  17127  evlsval  18741  madufval  19660  limcdif  22829  dfhnorm2  26773  cdj3lem3  28089  cdj3lem3b  28091  partfun  28280  esumsnf  28893  esumrnmpt2  28897  measinb2  29053  eulerpart  29223  fiblem  29239  trlset  33696  hoidmvlelem4  38324
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