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Mirrors > Home > MPE Home > Th. List > Mathboxes > sconntop | Structured version Visualization version Unicode version |
Description: A simply connected space is a topology. (Contributed by Mario Carneiro, 11-Feb-2015.) |
Ref | Expression |
---|---|
sconntop | SConn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sconnpconn 31209 | . 2 SConn PConn | |
2 | pconntop 31207 | . 2 PConn | |
3 | 1, 2 | syl 17 | 1 SConn |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wcel 1990 ctop 20698 PConncpconn 31201 SConncsconn 31202 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-iota 5851 df-fv 5896 df-ov 6653 df-pconn 31203 df-sconn 31204 |
This theorem is referenced by: sconnpi1 31221 txsconn 31223 cvmlift3lem6 31306 cvmlift3lem7 31307 cvmlift3lem8 31308 cvmlift3lem9 31309 |
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