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Theorem sconpcon 24914
 Description: A simply connected space is path-connected. (Contributed by Mario Carneiro, 11-Feb-2015.)
Assertion
Ref Expression
sconpcon SCon PCon

Proof of Theorem sconpcon
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 isscon 24913 . 2 SCon PCon
21simplbi 447 1 SCon PCon
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  wral 2705  csn 3814   class class class wbr 4212   cxp 4876  cfv 5454  (class class class)co 6081  cc0 8990  c1 8991  cicc 10919   ccn 17288  cii 18905   cphtpc 18994  PConcpcon 24906  SConcscon 24907 This theorem is referenced by:  scontop  24915  txscon  24928  rescon  24933  iinllycon  24941  cvmlift2lem10  24999  cvmlift3lem2  25007  cvmlift3  25015 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 2417 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 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-iota 5418  df-fv 5462  df-ov 6084  df-scon 24909
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