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Theorem fconst2 5977
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 5975 . 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 178    = wceq 1653    e. wcel 1727   _Vcvv 2962   {csn 3838    X. cxp 4905   -->wf 5479
This theorem is referenced by:  map1  7214  dvcmul  19861  plyeq0  20161  lnon0  22330  hsn0elch  22781  df0op2  23286  nmop0h  23525  xrge0mulc1cn  24358  lfl1  29966  lkr0f  29990
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-13 1729  ax-14 1731  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423  ax-sep 4355  ax-nul 4363  ax-pow 4406  ax-pr 4432
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2291  df-mo 2292  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ne 2607  df-ral 2716  df-rex 2717  df-rab 2720  df-v 2964  df-sbc 3168  df-csb 3268  df-dif 3309  df-un 3311  df-in 3313  df-ss 3320  df-nul 3614  df-if 3764  df-sn 3844  df-pr 3845  df-op 3847  df-uni 4040  df-br 4238  df-opab 4292  df-mpt 4293  df-id 4527  df-xp 4913  df-rel 4914  df-cnv 4915  df-co 4916  df-dm 4917  df-rn 4918  df-res 4919  df-ima 4920  df-iota 5447  df-fun 5485  df-fn 5486  df-f 5487  df-fv 5491
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