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Theorem scontop 27031
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 27030 . 2  |-  ( J  e. SCon  ->  J  e. PCon )
2 pcontop 27028 . 2  |-  ( J  e. PCon  ->  J  e.  Top )
31, 2syl 16 1  |-  ( J  e. SCon  ->  J  e.  Top )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    e. wcel 1761   Topctop 18398  PConcpcon 27022  SConcscon 27023
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1713  ax-7 1733  ax-10 1780  ax-11 1785  ax-12 1797  ax-13 1948  ax-ext 2422
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 962  df-tru 1367  df-ex 1592  df-nf 1595  df-sb 1706  df-clab 2428  df-cleq 2434  df-clel 2437  df-nfc 2566  df-ral 2718  df-rex 2719  df-rab 2722  df-v 2972  df-dif 3328  df-un 3330  df-in 3332  df-ss 3339  df-nul 3635  df-if 3789  df-sn 3875  df-pr 3877  df-op 3881  df-uni 4089  df-br 4290  df-iota 5378  df-fv 5423  df-ov 6093  df-pcon 27024  df-scon 27025
This theorem is referenced by:  sconpi1  27042  txscon  27044  cvmlift3lem6  27127  cvmlift3lem7  27128  cvmlift3lem8  27129  cvmlift3lem9  27130
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