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Theorem mpteq2i 4015
Description: An equality inference for the maps-to notation. (Contributed by Mario Carneiro, 16-Dec-2013.)
Hypothesis
Ref Expression
mpteq2i.1  |-  B  =  C
Assertion
Ref Expression
mpteq2i  |-  ( x  e.  A  |->  B )  =  ( x  e.  A  |->  C )

Proof of Theorem mpteq2i
StepHypRef Expression
1 mpteq2i.1 . . 3  |-  B  =  C
21a1i 9 . 2  |-  ( x  e.  A  ->  B  =  C )
32mpteq2ia 4014 1  |-  ( x  e.  A  |->  B )  =  ( x  e.  A  |->  C )
Colors of variables: wff set class
Syntax hints:    = wceq 1331    e. wcel 1480    |-> cmpt 3989
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-ral 2421  df-opab 3990  df-mpt 3991
This theorem is referenced by:  frecsuc  6304  fodjuomni  7021  fodjumkv  7034  axcaucvg  7715  0tonninf  10219  1tonninf  10220  cbvsum  11136  cbvprod  11334  eirraplem  11490  cnmpt12f  12465  fsumcncntop  12735  dvef  12866  nninfsellemqall  13241  nninfomni  13245  exmidsbthr  13248
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