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Theorem fconst2 5637
Description: A constant function expressed as a cross product. (Contributed by NM, 20-Aug-1999.)
Hypothesis
Ref Expression
fvconst2.1  |-  B  e. 
_V
Assertion
Ref Expression
fconst2  |-  ( F : A --> { B } 
<->  F  =  ( A  X.  { B }
) )

Proof of Theorem fconst2
StepHypRef Expression
1 fvconst2.1 . 2  |-  B  e. 
_V
2 fconst2g 5635 . 2  |-  ( B  e.  _V  ->  ( F : A --> { B } 
<->  F  =  ( A  X.  { B }
) ) )
31, 2ax-mp 5 1  |-  ( F : A --> { B } 
<->  F  =  ( A  X.  { B }
) )
Colors of variables: wff set class
Syntax hints:    <-> wb 104    = wceq 1331    e. wcel 1480   _Vcvv 2686   {csn 3527    X. cxp 4537   -->wf 5119
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-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-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046  ax-pow 4098  ax-pr 4131
This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-eu 2002  df-mo 2003  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422  df-v 2688  df-sbc 2910  df-csb 3004  df-un 3075  df-in 3077  df-ss 3084  df-pw 3512  df-sn 3533  df-pr 3534  df-op 3536  df-uni 3737  df-br 3930  df-opab 3990  df-mpt 3991  df-id 4215  df-xp 4545  df-rel 4546  df-cnv 4547  df-co 4548  df-dm 4549  df-rn 4550  df-iota 5088  df-fun 5125  df-fn 5126  df-f 5127  df-fv 5131
This theorem is referenced by:  map1  6706
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