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Theorem tfineq 4488
 Description: Equality theorem for the finite T operator. (Contributed by SF, 24-Jan-2015.)
Assertion
Ref Expression
tfineq Tfin Tfin

Proof of Theorem tfineq
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eqeq1 2359 . . 3
2 rexeq 2808 . . . . 5 1 1
32anbi2d 684 . . . 4 Nn 1 Nn 1
43iotabidv 4360 . . 3 Nn 1 Nn 1
51, 4ifbieq2d 3682 . 2 Nn 1 Nn 1
6 df-tfin 4443 . 2 Tfin Nn 1
7 df-tfin 4443 . 2 Tfin Nn 1
85, 6, 73eqtr4g 2410 1 Tfin Tfin
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 358   wceq 1642   wcel 1710  wrex 2615  c0 3550  cif 3662  1 cpw1 4135  cio 4337   Nn cnnc 4373   Tfin ctfin 4435 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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 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-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620  df-rab 2623  df-v 2861  df-nin 3211  df-compl 3212  df-un 3214  df-if 3663  df-uni 3892  df-iota 4339  df-tfin 4443 This theorem is referenced by:  tfincl  4492  tfin11  4493  tfin1c  4499  tfinltfinlem1  4500  tfinltfin  4501  eventfin  4517  oddtfin  4518  sfintfin  4532  tfinnn  4534  vfinncvntnn  4548  vfinspsslem1  4550  vfinspss  4551  vfinspclt  4552
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