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Theorem fatesg 24956
 Description: Equivalence of and in the case of quantifiers restricted to a singleton. (Contributed by FL, 1-Jun-2011.)
Assertion
Ref Expression
fatesg
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem fatesg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sneq 3651 . . 3
21raleqdv 2742 . 2
31rexeqdv 2743 . 2
4 vex 2791 . . 3
54fates 24955 . 2
62, 3, 5vtoclbg 2844 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wceq 1623   wcel 1684  wral 2543  wrex 2544  cvv 2788  csn 3640 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-rex 2549  df-v 2790  df-sn 3646
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