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Theorem scontop 24868
Description: A simply connected space is a topology. (Contributed by Mario Carneiro, 11-Feb-2015.)
Assertion
Ref Expression
scontop  |-  ( J  e. SCon  ->  J  e.  Top )

Proof of Theorem scontop
StepHypRef Expression
1 sconpcon 24867 . 2  |-  ( J  e. SCon  ->  J  e. PCon )
2 pcontop 24865 . 2  |-  ( J  e. PCon  ->  J  e.  Top )
31, 2syl 16 1  |-  ( J  e. SCon  ->  J  e.  Top )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1721   Topctop 16913  PConcpcon 24859  SConcscon 24860
This theorem is referenced by:  sconpi1  24879  txscon  24881  cvmlift3lem6  24964  cvmlift3lem7  24965  cvmlift3lem8  24966  cvmlift3lem9  24967
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-ral 2671  df-rex 2672  df-rab 2675  df-v 2918  df-dif 3283  df-un 3285  df-in 3287  df-ss 3294  df-nul 3589  df-if 3700  df-sn 3780  df-pr 3781  df-op 3783  df-uni 3976  df-br 4173  df-iota 5377  df-fv 5421  df-ov 6043  df-pcon 24861  df-scon 24862
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