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Theorem mpteq12i 4253
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 4247 . 2  |-  (  T. 
->  ( x  e.  A  |->  B )  =  ( x  e.  C  |->  D ) )
65trud 1329 1  |-  ( x  e.  A  |->  B )  =  ( x  e.  C  |->  D )
Colors of variables: wff set class
Syntax hints:    T. wtru 1322    = wceq 1649    e. cmpt 4226
This theorem is referenced by:  offres  6278  limcdif  19716  evlsval  19893  dfhnorm2  22577  cdj3lem3  23894  cdj3lem3b  23896  partfun  24040  esumsn  24409  measinb2  24530  trlset  30643
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-ral 2671  df-opab 4227  df-mpt 4228
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