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

Theorem iotacl 5079
 Description: Membership law for descriptions. This can useful for expanding an unbounded iota-based definition (see df-iota 5056). (Contributed by Andrew Salmon, 1-Aug-2011.)
Assertion
Ref Expression
iotacl

Proof of Theorem iotacl
StepHypRef Expression
1 iota4 5074 . 2
2 df-sbc 2881 . 2
31, 2sylib 121 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1463  weu 1975  cab 2101  wsbc 2880  cio 5054 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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-eu 1978  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-rex 2397  df-v 2660  df-sbc 2881  df-un 3043  df-sn 3501  df-pr 3502  df-uni 3705  df-iota 5056 This theorem is referenced by:  riotacl2  5709  eroprf  6488
 Copyright terms: Public domain W3C validator