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Theorem mpteq12i 4293
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 4287 . 2  |-  (  T. 
->  ( x  e.  A  |->  B )  =  ( x  e.  C  |->  D ) )
65trud 1332 1  |-  ( x  e.  A  |->  B )  =  ( x  e.  C  |->  D )
Colors of variables: wff set class
Syntax hints:    T. wtru 1325    = wceq 1652    e. cmpt 4266
This theorem is referenced by:  offres  6319  limcdif  19763  evlsval  19940  dfhnorm2  22624  cdj3lem3  23941  cdj3lem3b  23943  partfun  24087  esumsn  24456  measinb2  24577  trlset  30958
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-ral 2710  df-opab 4267  df-mpt 4268
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