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Theorem scontop 23774
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 23773 . 2  |-  ( J  e. SCon  ->  J  e. PCon )
2 pcontop 23771 . 2  |-  ( J  e. PCon  ->  J  e.  Top )
31, 2syl 15 1  |-  ( J  e. SCon  ->  J  e.  Top )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1696   Topctop 16647  PConcpcon 23765  SConcscon 23766
This theorem is referenced by:  sconpi1  23785  txscon  23787  cvmlift3lem6  23870  cvmlift3lem7  23871  cvmlift3lem8  23872  cvmlift3lem9  23873
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-iota 5235  df-fv 5279  df-ov 5877  df-pcon 23767  df-scon 23768
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