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Theorem scontop 29512
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 29511 . 2  |-  ( J  e. SCon  ->  J  e. PCon )
2 pcontop 29509 . 2  |-  ( J  e. PCon  ->  J  e.  Top )
31, 2syl 17 1  |-  ( J  e. SCon  ->  J  e.  Top )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    e. wcel 1842   Topctop 19684  PConcpcon 29503  SConcscon 29504
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 976  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ral 2758  df-rex 2759  df-rab 2762  df-v 3060  df-dif 3416  df-un 3418  df-in 3420  df-ss 3427  df-nul 3738  df-if 3885  df-sn 3972  df-pr 3974  df-op 3978  df-uni 4191  df-br 4395  df-iota 5532  df-fv 5576  df-ov 6280  df-pcon 29505  df-scon 29506
This theorem is referenced by:  sconpi1  29523  txscon  29525  cvmlift3lem6  29608  cvmlift3lem7  29609  cvmlift3lem8  29610  cvmlift3lem9  29611
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