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Theorem ist1 19949
 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 4259 . . . . . 6
2 ist0.1 . . . . . 6
31, 2syl6eqr 2516 . . . . 5
43eleq2d 2527 . . . 4
5 fveq2 5872 . . . . 5
65eleq2d 2527 . . . 4
74, 6imbi12d 320 . . 3
87ralbidv2 2892 . 2
9 df-t1 19942 . 2
108, 9elrab2 3259 1
 Colors of variables: wff setvar class Syntax hints:   wb 184   wa 369   wceq 1395   wcel 1819  wral 2807  csn 4032  cuni 4251  cfv 5594  ctop 19521  ccld 19644  ct1 19935 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-t1 19942 This theorem is referenced by:  t1sncld  19954  t1ficld  19955  t1top  19958  ist1-2  19975  cnt1  19978  ordtt1  20007  qtopt1  27999  onint1  30098
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