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Theorem tfinex 4485
 Description: The finite T operator is always a set. (Contributed by SF, 26-Jan-2015.)
Assertion
Ref Expression
tfinex Tfin A V

Proof of Theorem tfinex
Dummy variables x y are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-tfin 4443 . 2 Tfin A = if(A = , , (℩x(x Nn y A 1y x)))
2 0ex 4110 . . 3 V
3 iotaex 4356 . . 3 (℩x(x Nn y A 1y x)) V
42, 3ifex 3720 . 2 if(A = , , (℩x(x Nn y A 1y x))) V
51, 4eqeltri 2423 1 Tfin A V
 Colors of variables: wff setvar class Syntax hints:   ∧ wa 358   = wceq 1642   ∈ wcel 1710  ∃wrex 2615  Vcvv 2859  ∅c0 3550   ifcif 3662  ℘1cpw1 4135  ℩cio 4337   Nn cnnc 4373   Tfin ctfin 4435 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  ax-nin 4078 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-ral 2619  df-rex 2620  df-v 2861  df-sbc 3047  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-ss 3259  df-nul 3551  df-if 3663  df-sn 3741  df-pr 3742  df-uni 3892  df-iota 4339  df-tfin 4443 This theorem is referenced by:  tfinltfinlem1  4500  tfinltfin  4501  eventfin  4517  oddtfin  4518  sfintfinlem1  4531  tfinnnlem1  4533  tfinnn  4534  vfinspsslem1  4550
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