ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  mpteq2i Unicode version

Theorem mpteq2i 3894
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 3893 1  |-  ( x  e.  A  |->  B )  =  ( x  e.  A  |->  C )
Colors of variables: wff set class
Syntax hints:    = wceq 1287    e. wcel 1436    |-> cmpt 3868
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-11 1440  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-ral 2360  df-opab 3869  df-mpt 3870
This theorem is referenced by:  frecsuc  6107  fodjuomni  6725  axcaucvg  7356  0tonninf  9748  1tonninf  9749  nninfsellemqall  11263  nninfomni  11267  exmidsbthr  11269
  Copyright terms: Public domain W3C validator