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

Theorem mpteq2i 3985
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 3984 1  |-  ( x  e.  A  |->  B )  =  ( x  e.  A  |->  C )
Colors of variables: wff set class
Syntax hints:    = wceq 1316    e. wcel 1465    |-> cmpt 3959
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 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-11 1469  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-ral 2398  df-opab 3960  df-mpt 3961
This theorem is referenced by:  frecsuc  6272  fodjuomni  6989  fodjumkv  7002  axcaucvg  7676  0tonninf  10180  1tonninf  10181  cbvsum  11097  eirraplem  11410  cnmpt12f  12382  fsumcncntop  12652  dvef  12783  nninfsellemqall  13138  nninfomni  13142  exmidsbthr  13145
  Copyright terms: Public domain W3C validator