Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  prid1g Unicode version

Theorem prid1g 3663
 Description: An unordered pair contains its first member. Part of Theorem 7.6 of [Quine] p. 49. (Contributed by Stefan Allan, 8-Nov-2008.)
Assertion
Ref Expression
prid1g

Proof of Theorem prid1g
StepHypRef Expression
1 eqid 2157 . . 3
21orci 721 . 2
3 elprg 3580 . 2
42, 3mpbiri 167 1
 Colors of variables: wff set class Syntax hints:   wi 4   wo 698   wceq 1335   wcel 2128  cpr 3561 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 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-un 3106  df-sn 3566  df-pr 3567 This theorem is referenced by:  prid2g  3664  prid1  3665  preqr1g  3729  opth1  4195  en2lp  4511  acexmidlemcase  5813  en2eqpr  6845  m1expcl2  10423  maxabslemval  11090  xrmaxiflemval  11129  xrmaxaddlem  11139  2strbasg  12251  2strbas1g  12254  coseq0negpitopi  13117
 Copyright terms: Public domain W3C validator