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Theorem ufli 17948
 Description: Property of a set that satifies the ultrafilter lemma. (Contributed by Mario Carneiro, 26-Aug-2015.)
Assertion
Ref Expression
ufli UFL
Distinct variable groups:   ,   ,

Proof of Theorem ufli
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 isufl 17947 . . 3 UFL UFL
21ibi 234 . 2 UFL
3 sseq1 3371 . . . 4
43rexbidv 2728 . . 3
54rspccva 3053 . 2
62, 5sylan 459 1 UFL
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1653   wcel 1726  wral 2707  wrex 2708   wss 3322  cfv 5456  cfil 17879  cufil 17933  UFLcufl 17934 This theorem is referenced by:  ssufl  17952  ufldom  17996  ufilcmp  18066 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-iota 5420  df-fv 5464  df-ufl 17936
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