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Theorem isscon 24915
 Description: The property of being a simply connected topological space. (Contributed by Mario Carneiro, 11-Feb-2015.)
Assertion
Ref Expression
isscon SCon PCon
Distinct variable group:   ,

Proof of Theorem isscon
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 oveq2 6091 . . 3
2 fveq2 5730 . . . . 5
32breqd 4225 . . . 4
43imbi2d 309 . . 3
51, 4raleqbidv 2918 . 2
6 df-scon 24911 . 2 SCon PCon
75, 6elrab2 3096 1 SCon PCon
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   wceq 1653   wcel 1726  wral 2707  csn 3816   class class class wbr 4214   cxp 4878  cfv 5456  (class class class)co 6083  cc0 8992  c1 8993  cicc 10921   ccn 17290  cii 18907   cphtpc 18996  PConcpcon 24908  SConcscon 24909 This theorem is referenced by:  sconpcon  24916  sconpht  24918  sconpi1  24928  txscon  24930  cvxscon  24932 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-iota 5420  df-fv 5464  df-ov 6086  df-scon 24911
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