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

Theorem euiotaex 5116
 Description: Theorem 8.23 in [Quine] p. 58, with existential uniqueness condition added. This theorem proves the existence of the class under our definition. (Contributed by Jim Kingdon, 21-Dec-2018.)
Assertion
Ref Expression
euiotaex

Proof of Theorem euiotaex
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 iotaval 5111 . . . 4
21eqcomd 2147 . . 3
32eximi 1576 . 2
4 df-eu 1993 . 2
5 isset 2697 . 2
63, 4, 53imtr4i 200 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104  wal 1330   wceq 1332  wex 1469  weu 1990   wcel 2112  cvv 2691  cio 5098 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 2123 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1732  df-eu 1993  df-clab 2128  df-cleq 2134  df-clel 2137  df-nfc 2272  df-rex 2424  df-v 2693  df-sbc 2916  df-un 3082  df-sn 3540  df-pr 3541  df-uni 3747  df-iota 5100 This theorem is referenced by:  iota4an  5119  funfvex  5450
 Copyright terms: Public domain W3C validator