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Theorem issetf 2864
 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 2863 . 2 (A V ↔ y y = A)
2 issetf.1 . . . 4 xA
32nfeq2 2500 . . 3 x y = A
4 nfv 1619 . . 3 y x = A
5 eqeq1 2359 . . 3 (y = x → (y = Ax = A))
63, 4, 5cbvex 1985 . 2 (y y = Ax x = A)
71, 6bitri 240 1 (A V ↔ x x = A)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176  ∃wex 1541   = wceq 1642   ∈ wcel 1710  Ⅎwnfc 2476  Vcvv 2859 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861 This theorem is referenced by:  vtoclgf  2913  spcimgft  2930
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