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Theorem issetf 2539
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 xA
Assertion
Ref Expression
issetf (A V ↔ x x = A)

Proof of Theorem issetf
Dummy variable y is distinct from all other variables.
StepHypRef Expression
1 isset 2538 . 2 (A V ↔ y y = A)
2 issetf.1 . . . 4 xA
32nfeq2 2172 . . 3 x y = A
4 nfv 1404 . . 3 y x = A
5 eqeq1 2029 . . 3 (y = x → (y = Ax = A))
63, 4, 5cbvex 1622 . 2 (y y = Ax x = A)
71, 6bitri 173 1 (A V ↔ x x = A)
Colors of variables: wff set class
Syntax hints:  wb 98  wex 1362   = wceq 1374   wcel 1376  wnfc 2148  Vcvv 2534
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 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1378  ax-10 1379  ax-11 1380  ax-i12 1381  ax-bnd 1382  ax-4 1383  ax-17 1402  ax-i9 1406  ax-ial 1411  ax-i5r 1412  ax-ext 2005
This theorem depends on definitions:  df-bi 110  df-tru 1232  df-nf 1330  df-sb 1629  df-clab 2010  df-cleq 2016  df-clel 2019  df-nfc 2150  df-v 2536
This theorem is referenced by:  vtoclgf  2588  spcimgft  2605  spcimegft  2607
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