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Theorem ist1 17377
 Description: The predicate is T1. (Contributed by FL, 18-Jun-2007.)
Hypothesis
Ref Expression
ist0.1
Assertion
Ref Expression
ist1
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem ist1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 unieq 4016 . . . . . 6
2 ist0.1 . . . . . 6
31, 2syl6eqr 2485 . . . . 5
43eleq2d 2502 . . . 4
5 fveq2 5720 . . . . 5
65eleq2d 2502 . . . 4
74, 6imbi12d 312 . . 3
87ralbidv2 2719 . 2
9 df-t1 17370 . 2
108, 9elrab2 3086 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359   wceq 1652   wcel 1725  wral 2697  csn 3806  cuni 4007  cfv 5446  ctop 16950  ccld 17072  ct1 17363 This theorem is referenced by:  t1sncld  17382  t1ficld  17383  t1top  17386  ist1-2  17403  cnt1  17406  ordtt1  17435  onint1  26191 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-t1 17370
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