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Theorem iscon 20363
 Description: The predicate is a connected topology . (Contributed by FL, 17-Nov-2008.)
Hypothesis
Ref Expression
iscon.1
Assertion
Ref Expression
iscon

Proof of Theorem iscon
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 id 22 . . . 4
2 fveq2 5818 . . . 4
31, 2ineq12d 3601 . . 3
4 unieq 4163 . . . . 5
5 iscon.1 . . . . 5
64, 5syl6eqr 2474 . . . 4
76preq2d 4022 . . 3
83, 7eqeq12d 2437 . 2
9 df-con 20362 . 2
108, 9elrab2 3166 1
 Colors of variables: wff setvar class Syntax hints:   wb 187   wa 370   wceq 1437   wcel 1872   cin 3371  c0 3697  cpr 3936  cuni 4155  cfv 5537  ctop 19852  ccld 19966  ccon 20361 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2058  ax-ext 2402 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2409  df-cleq 2415  df-clel 2418  df-nfc 2552  df-rex 2714  df-rab 2717  df-v 3018  df-dif 3375  df-un 3377  df-in 3379  df-ss 3386  df-nul 3698  df-if 3848  df-sn 3935  df-pr 3937  df-op 3941  df-uni 4156  df-br 4360  df-iota 5501  df-fv 5545  df-con 20362 This theorem is referenced by:  iscon2  20364  conclo  20365  conndisj  20366  contop  20367
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