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Theorem mposnif 5858
Description: A mapping with two arguments with the first argument from a singleton and a conditional as result. (Contributed by AV, 14-Feb-2019.)
Assertion
Ref Expression
mposnif  |-  ( i  e.  { X } ,  j  e.  B  |->  if ( i  =  X ,  C ,  D ) )  =  ( i  e.  { X } ,  j  e.  B  |->  C )

Proof of Theorem mposnif
StepHypRef Expression
1 elsni 3540 . . . 4  |-  ( i  e.  { X }  ->  i  =  X )
21adantr 274 . . 3  |-  ( ( i  e.  { X }  /\  j  e.  B
)  ->  i  =  X )
32iftrued 3476 . 2  |-  ( ( i  e.  { X }  /\  j  e.  B
)  ->  if (
i  =  X ,  C ,  D )  =  C )
43mpoeq3ia 5829 1  |-  ( i  e.  { X } ,  j  e.  B  |->  if ( i  =  X ,  C ,  D ) )  =  ( i  e.  { X } ,  j  e.  B  |->  C )
Colors of variables: wff set class
Syntax hints:    /\ wa 103    = wceq 1331    e. wcel 1480   ifcif 3469   {csn 3522    e. cmpo 5769
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-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119
This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-if 3470  df-sn 3528  df-oprab 5771  df-mpo 5772
This theorem is referenced by: (None)
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