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Theorem issetf 2921
 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 2920 . 2
2 issetf.1 . . . 4
32nfeq2 2551 . . 3
4 nfv 1626 . . 3
5 eqeq1 2410 . . 3
63, 4, 5cbvex 2038 . 2
71, 6bitri 241 1
 Colors of variables: wff set class Syntax hints:   wb 177  wex 1547   wceq 1649   wcel 1721  wnfc 2527  cvv 2916 This theorem is referenced by:  vtoclgf  2970  spcimgft  2987 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-v 2918
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