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Theorem fconst2 5746
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 5744 . 2  |-  ( B  e.  _V  ->  ( F : A --> { B } 
<->  F  =  ( A  X.  { B }
) ) )
31, 2ax-mp 8 1  |-  ( F : A --> { B } 
<->  F  =  ( A  X.  { B }
) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    = wceq 1632    e. wcel 1696   _Vcvv 2801   {csn 3653    X. cxp 4703   -->wf 5267
This theorem is referenced by:  map1  6955  dvcmul  19309  plyeq0  19609  lnon0  21392  hsn0elch  21843  df0op2  22348  nmop0h  22587  xrge0mulc1cn  23338  lfl1  29882  lkr0f  29906
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-13 1698  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pow 4204  ax-pr 4230
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-sbc 3005  df-csb 3095  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-opab 4094  df-mpt 4095  df-id 4325  df-xp 4711  df-rel 4712  df-cnv 4713  df-co 4714  df-dm 4715  df-rn 4716  df-res 4717  df-ima 4718  df-iota 5235  df-fun 5273  df-fn 5274  df-f 5275  df-fv 5279
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