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Theorem tlmtps 22502
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 22501 . 2 (𝑊 ∈ TopMod → 𝑊 ∈ TopMnd)
2 tmdtps 22391 . 2 (𝑊 ∈ TopMnd → 𝑊 ∈ TopSp)
31, 2syl 17 1 (𝑊 ∈ TopMod → 𝑊 ∈ TopSp)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2050  TopSpctps 21247  TopMndctmd 22385  TopModctlm 22472
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1965  ax-8 2052  ax-9 2059  ax-10 2079  ax-11 2093  ax-12 2106  ax-ext 2750  ax-nul 5068
This theorem depends on definitions:  df-bi 199  df-an 388  df-or 834  df-3an 1070  df-tru 1510  df-ex 1743  df-nf 1747  df-sb 2016  df-mo 2547  df-eu 2583  df-clab 2759  df-cleq 2771  df-clel 2846  df-nfc 2918  df-ral 3093  df-rex 3094  df-rab 3097  df-v 3417  df-sbc 3684  df-dif 3834  df-un 3836  df-in 3838  df-ss 3845  df-nul 4181  df-if 4352  df-sn 4443  df-pr 4445  df-op 4449  df-uni 4714  df-br 4931  df-iota 6154  df-fv 6198  df-ov 6981  df-tmd 22387  df-tlm 22476
This theorem is referenced by:  cnmpt1vsca  22508  cnmpt2vsca  22509  tlmtgp  22510
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