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

Theorem issetf 2556
 Description: A version of isset that does not require x and A to be distinct. (Contributed by Andrew Salmon, 6-Jun-2011.) (Revised by Mario Carneiro, 10-Oct-2016.)
Hypothesis
Ref Expression
issetf.1
Assertion
Ref Expression
issetf

Proof of Theorem issetf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 isset 2555 . 2
2 issetf.1 . . . 4
32nfeq2 2186 . . 3
4 nfv 1418 . . 3
5 eqeq1 2043 . . 3
63, 4, 5cbvex 1636 . 2
71, 6bitri 173 1
 Colors of variables: wff set class Syntax hints:   wb 98   wceq 1242  wex 1378   wcel 1390  wnfc 2162  cvv 2551 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553 This theorem is referenced by:  vtoclgf  2606  spcimgft  2623  spcimegft  2625  bj-vtoclgft  9249
 Copyright terms: Public domain W3C validator