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Theorem prfOLD 25514
Description: A function with a domain of two elements. (Moved to fpr 5742 in main set.mm and may be deleted by mathbox owner, JM. --NM 3-Sep-2011.) (Contributed by Jeff Madsen, 20-Jun-2010.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
prf.1  |-  A  e. 
_V
prf.2  |-  B  e. 
_V
prf.3  |-  C  e. 
_V
prf.4  |-  D  e. 
_V
Assertion
Ref Expression
prfOLD  |-  ( A  =/=  B  ->  { <. A ,  C >. ,  <. B ,  D >. } : { A ,  B } --> { C ,  D }
)

Proof of Theorem prfOLD
StepHypRef Expression
1 prf.1 . 2  |-  A  e. 
_V
2 prf.2 . 2  |-  B  e. 
_V
3 prf.3 . 2  |-  C  e. 
_V
4 prf.4 . 2  |-  D  e. 
_V
51, 2, 3, 4fpr 5742 1  |-  ( A  =/=  B  ->  { <. A ,  C >. ,  <. B ,  D >. } : { A ,  B } --> { C ,  D }
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1701    =/= wne 2479   _Vcvv 2822   {cpr 3675   <.cop 3677   -->wf 5288
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1537  ax-5 1548  ax-17 1607  ax-9 1645  ax-8 1666  ax-14 1705  ax-6 1720  ax-7 1725  ax-11 1732  ax-12 1897  ax-ext 2297  ax-sep 4178  ax-nul 4186  ax-pr 4251
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1533  df-nf 1536  df-sb 1640  df-eu 2180  df-mo 2181  df-clab 2303  df-cleq 2309  df-clel 2312  df-nfc 2441  df-ne 2481  df-ral 2582  df-rex 2583  df-rab 2586  df-v 2824  df-dif 3189  df-un 3191  df-in 3193  df-ss 3200  df-nul 3490  df-if 3600  df-sn 3680  df-pr 3681  df-op 3683  df-br 4061  df-opab 4115  df-id 4346  df-xp 4732  df-rel 4733  df-cnv 4734  df-co 4735  df-dm 4736  df-rn 4737  df-fun 5294  df-fn 5295  df-f 5296
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