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Theorem ufli 20541
 Description: Property of a set that satisfies 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 20540 . . 3 UFL UFL
21ibi 241 . 2 UFL
3 sseq1 3520 . . . 4
43rexbidv 2968 . . 3
54rspccva 3209 . 2
62, 5sylan 471 1 UFL
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   wceq 1395   wcel 1819  wral 2807  wrex 2808   wss 3471  cfv 5594  cfil 20472  cufil 20526  UFLcufl 20527 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-nul 3794  df-if 3945  df-sn 4033  df-pr 4035  df-op 4039  df-uni 4252  df-br 4457  df-iota 5557  df-fv 5602  df-ufl 20529 This theorem is referenced by:  ssufl  20545  ufldom  20589  ufilcmp  20659
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