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Theorem prid2 3534
Description: An unordered pair contains its second member. Part of Theorem 7.6 of [Quine] p. 49. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
prid2.1  |-  B  e. 
_V
Assertion
Ref Expression
prid2  |-  B  e. 
{ A ,  B }

Proof of Theorem prid2
StepHypRef Expression
1 prid2.1 . . 3  |-  B  e. 
_V
21prid1 3533 . 2  |-  B  e. 
{ B ,  A }
3 prcom 3503 . 2  |-  { B ,  A }  =  { A ,  B }
42, 3eleqtri 2159 1  |-  B  e. 
{ A ,  B }
Colors of variables: wff set class
Syntax hints:    e. wcel 1436   _Vcvv 2615   {cpr 3432
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 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-v 2617  df-un 2992  df-sn 3437  df-pr 3438
This theorem is referenced by:  prel12  3600  opi2  4036  opeluu  4248  ontr2exmid  4316  onsucelsucexmid  4321  regexmidlemm  4323  ordtri2or2exmid  4362  dmrnssfld  4666  funopg  5015  acexmidlema  5606  acexmidlemcase  5610  acexmidlem2  5612  2dom  6476  unfiexmid  6582  djuss  6708  fodjuomnilemf  6747  exmidfodomrlemr  6775  exmidfodomrlemrALT  6776  cnelprrecn  7425  mnfxr  7491  m1expcl2  9897  bdop  11254  1lt2o  11374
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