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Theorem rnsnop 4898
Description: The range of a singleton of an ordered pair is the singleton of the second member. (Contributed by NM, 24-Jul-2004.) (Revised by Mario Carneiro, 26-Apr-2015.)
Hypothesis
Ref Expression
cnvsn.1  |-  A  e. 
_V
Assertion
Ref Expression
rnsnop  |-  ran  { <. A ,  B >. }  =  { B }

Proof of Theorem rnsnop
StepHypRef Expression
1 cnvsn.1 . 2  |-  A  e. 
_V
2 rnsnopg 4896 . 2  |-  ( A  e.  _V  ->  ran  {
<. A ,  B >. }  =  { B }
)
31, 2ax-mp 7 1  |-  ran  { <. A ,  B >. }  =  { B }
Colors of variables: wff set class
Syntax hints:    = wceq 1289    e. wcel 1438   _Vcvv 2619   {csn 3441   <.cop 3444   ran crn 4429
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-14 1450  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-sep 3949  ax-pow 4001  ax-pr 4027
This theorem depends on definitions:  df-bi 115  df-3an 926  df-tru 1292  df-nf 1395  df-sb 1693  df-eu 1951  df-mo 1952  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-ral 2364  df-rex 2365  df-v 2621  df-un 3001  df-in 3003  df-ss 3010  df-pw 3427  df-sn 3447  df-pr 3448  df-op 3450  df-br 3838  df-opab 3892  df-xp 4434  df-rel 4435  df-cnv 4436  df-dm 4438  df-rn 4439
This theorem is referenced by:  op2nda  4902  fpr  5463  en1  6496
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