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Theorem tlmtps 17972
Description: A topological module is a topological space. (Contributed by Mario Carneiro, 5-Oct-2015.)
Assertion
Ref Expression
tlmtps  |-  ( W  e. TopMod  ->  W  e.  TopSp )

Proof of Theorem tlmtps
StepHypRef Expression
1 tlmtmd 17971 . 2  |-  ( W  e. TopMod  ->  W  e. TopMnd )
2 tmdtps 17861 . 2  |-  ( W  e. TopMnd  ->  W  e.  TopSp )
31, 2syl 15 1  |-  ( W  e. TopMod  ->  W  e.  TopSp )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1710   TopSpctps 16740  TopMndctmd 17855  TopModctlm 17942
This theorem is referenced by:  cnmpt1vsca  17978  cnmpt2vsca  17979  tlmtgp  17980
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930  ax-ext 2339  ax-nul 4230
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2213  df-clab 2345  df-cleq 2351  df-clel 2354  df-nfc 2483  df-ne 2523  df-ral 2624  df-rex 2625  df-rab 2628  df-v 2866  df-sbc 3068  df-dif 3231  df-un 3233  df-in 3235  df-ss 3242  df-nul 3532  df-if 3642  df-sn 3722  df-pr 3723  df-op 3725  df-uni 3909  df-br 4105  df-iota 5301  df-fv 5345  df-ov 5948  df-tmd 17857  df-tlm 17946
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