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Theorem mpteq12i 4103
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 9 . . 3  |-  ( T. 
->  A  =  C
)
3 mpteq12i.2 . . . 4  |-  B  =  D
43a1i 9 . . 3  |-  ( T. 
->  B  =  D
)
52, 4mpteq12dv 4097 . 2  |-  ( T. 
->  ( x  e.  A  |->  B )  =  ( x  e.  C  |->  D ) )
65mptru 1372 1  |-  ( x  e.  A  |->  B )  =  ( x  e.  C  |->  D )
Colors of variables: wff set class
Syntax hints:    = wceq 1363   T. wtru 1364    |-> cmpt 4076
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-11 1516  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169
This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-ral 2470  df-opab 4077  df-mpt 4078
This theorem is referenced by:  offres  6149
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