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Theorem isufl 17937
 Description: Define the (strong) ultrafilter lemma, parameterized over base sets. A set satisfies the ultrafilter lemma if every filter on is a subset of some ultrafilter. (Contributed by Mario Carneiro, 26-Aug-2015.)
Assertion
Ref Expression
isufl UFL
Distinct variable group:   ,,
Allowed substitution hints:   (,)

Proof of Theorem isufl
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 fveq2 5720 . . 3
2 fveq2 5720 . . . 4
32rexeqdv 2903 . . 3
41, 3raleqbidv 2908 . 2
5 df-ufl 17926 . 2 UFL
64, 5elab2g 3076 1 UFL
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wceq 1652   wcel 1725  wral 2697  wrex 2698   wss 3312  cfv 5446  cfil 17869  cufil 17923  UFLcufl 17924 This theorem is referenced by:  ufli  17938  numufl  17939  ssufl  17942  ufldom  17986 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-iota 5410  df-fv 5454  df-ufl 17926
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