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Theorem mpteq12i 4104
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 10 . . 3  |-  (  T. 
->  A  =  C
)
3 mpteq12i.2 . . . 4  |-  B  =  D
43a1i 10 . . 3  |-  (  T. 
->  B  =  D
)
52, 4mpteq12dv 4098 . 2  |-  (  T. 
->  ( x  e.  A  |->  B )  =  ( x  e.  C  |->  D ) )
65trud 1314 1  |-  ( x  e.  A  |->  B )  =  ( x  e.  C  |->  D )
Colors of variables: wff set class
Syntax hints:    T. wtru 1307    = wceq 1623    e. cmpt 4077
This theorem is referenced by:  offres  6092  limcdif  19226  evlsval  19403  dfhnorm2  21701  cdj3lem3  23018  cdj3lem3b  23020  partfun  23240  esumsn  23437  measinb2  23550  trlset  30350
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-ral 2548  df-opab 4078  df-mpt 4079
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