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Theorem tlmtps 24036
Description: A topological module is a topological space. (Contributed by Mario Carneiro, 5-Oct-2015.)
Assertion
Ref Expression
tlmtps (𝑊 ∈ TopMod → 𝑊 ∈ TopSp)

Proof of Theorem tlmtps
StepHypRef Expression
1 tlmtmd 24035 . 2 (𝑊 ∈ TopMod → 𝑊 ∈ TopMnd)
2 tmdtps 23924 . 2 (𝑊 ∈ TopMnd → 𝑊 ∈ TopSp)
31, 2syl 17 1 (𝑊 ∈ TopMod → 𝑊 ∈ TopSp)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2098  TopSpctps 22778  TopMndctmd 23918  TopModctlm 24006
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695  ax-nul 5297
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-ne 2933  df-rab 3425  df-v 3468  df-sbc 3771  df-dif 3944  df-un 3946  df-in 3948  df-ss 3958  df-nul 4316  df-if 4522  df-sn 4622  df-pr 4624  df-op 4628  df-uni 4901  df-br 5140  df-iota 6486  df-fv 6542  df-ov 7405  df-tmd 23920  df-tlm 24010
This theorem is referenced by:  cnmpt1vsca  24042  cnmpt2vsca  24043  tlmtgp  24044
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