Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  dfsn2 Unicode version

Theorem dfsn2 3480
 Description: Alternate definition of singleton. Definition 5.1 of [TakeutiZaring] p. 15. (Contributed by NM, 24-Apr-1994.)
Assertion
Ref Expression
dfsn2

Proof of Theorem dfsn2
StepHypRef Expression
1 df-pr 3473 . 2
2 unidm 3158 . 2
31, 2eqtr2i 2116 1
 Colors of variables: wff set class Syntax hints:   wceq 1296   cun 3011  csn 3466  cpr 3467 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077 This theorem depends on definitions:  df-bi 116  df-tru 1299  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-nfc 2224  df-v 2635  df-un 3017  df-pr 3473 This theorem is referenced by:  nfsn  3522  tpidm12  3561  tpidm  3564  preqsn  3641  opid  3662  unisn  3691  intsng  3744  opeqsn  4103  relop  4617  funopg  5082  enpr1g  6595  hashprg  10331  bj-snexg  12520
 Copyright terms: Public domain W3C validator