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Theorem prid2 3662
 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
Assertion
Ref Expression
prid2

Proof of Theorem prid2
StepHypRef Expression
1 prid2.1 . . 3
21prid1 3661 . 2
3 prcom 3631 . 2
42, 3eleqtri 2229 1
 Colors of variables: wff set class Syntax hints:   wcel 2125  cvv 2709  cpr 3557 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-v 2711  df-un 3102  df-sn 3562  df-pr 3563 This theorem is referenced by:  prel12  3730  opi2  4188  opeluu  4404  ontr2exmid  4478  onsucelsucexmid  4483  regexmidlemm  4485  ordtri2or2exmid  4524  ontri2orexmidim  4525  dmrnssfld  4842  funopg  5197  acexmidlema  5805  acexmidlemcase  5809  acexmidlem2  5811  1lt2o  6379  2dom  6739  unfiexmid  6851  djuss  7000  exmidonfinlem  7107  exmidfodomrlemr  7116  exmidfodomrlemrALT  7117  exmidaclem  7122  cnelprrecn  7847  mnfxr  7913  sup3exmid  8807  m1expcl2  10419  bdop  13388  2o01f  13507  iswomni0  13563
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