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Theorem mpteq2i 3871
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 3870 1  |-  ( x  e.  A  |->  B )  =  ( x  e.  A  |->  C )
Colors of variables: wff set class
Syntax hints:    = wceq 1259    e. wcel 1409    |-> cmpt 3845
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-ral 2328  df-opab 3846  df-mpt 3847
This theorem is referenced by:  frecsuc  6021  axcaucvg  7031
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