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

Theorem rext 4146
 Description: A theorem similar to extensionality, requiring the existence of a singleton. Exercise 8 of [TakeutiZaring] p. 16. (Contributed by NM, 10-Aug-1993.)
Assertion
Ref Expression
rext
Distinct variable group:   ,,

Proof of Theorem rext
StepHypRef Expression
1 vsnid 3565 . . 3
2 vex 2693 . . . . 5
32snex 4118 . . . 4
4 eleq2 2204 . . . . 5
5 eleq2 2204 . . . . 5
64, 5imbi12d 233 . . . 4
73, 6spcv 2784 . . 3
81, 7mpi 15 . 2
9 velsn 3550 . . 3
10 equcomi 1681 . . 3
119, 10sylbi 120 . 2
128, 11syl 14 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1330   wceq 1332   wcel 1481  csn 3533 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 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-14 1493  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122  ax-sep 4055  ax-pow 4107 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2692  df-in 3083  df-ss 3090  df-pw 3518  df-sn 3539 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator