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Theorem fconst2 6108
Description: A constant function expressed as a Cartesian 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 6106 . 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 setvar class
Syntax hints:    <-> wb 184    = wceq 1374    e. wcel 1762   _Vcvv 3106   {csn 4020    X. cxp 4990   -->wf 5575
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-8 1764  ax-9 1766  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1961  ax-ext 2438  ax-sep 4561  ax-nul 4569  ax-pow 4618  ax-pr 4679
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 970  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-eu 2272  df-mo 2273  df-clab 2446  df-cleq 2452  df-clel 2455  df-nfc 2610  df-ne 2657  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3108  df-sbc 3325  df-csb 3429  df-dif 3472  df-un 3474  df-in 3476  df-ss 3483  df-nul 3779  df-if 3933  df-sn 4021  df-pr 4023  df-op 4027  df-uni 4239  df-br 4441  df-opab 4499  df-mpt 4500  df-id 4788  df-xp 4998  df-rel 4999  df-cnv 5000  df-co 5001  df-dm 5002  df-rn 5003  df-res 5004  df-ima 5005  df-iota 5542  df-fun 5581  df-fn 5582  df-f 5583  df-fv 5587
This theorem is referenced by:  map1  7584  rrxcph  21552  dvcmul  22075  plyeq0  22336  lnon0  25239  hsn0elch  25692  df0op2  26197  nmop0h  26436  xrge0mulc1cn  27409  lindsrng01  32017  lfl1  33742  lkr0f  33766
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