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Theorem txtopiOLD 25652
Description: The product of two topologies is a topology. (Moved to txtopi 17117 in main set.mm and may be deleted by mathbox owner, JM. --NM 15-Oct-2012.) (Contributed by Jeff Madsen, 15-Jun-2010.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
txtopiOLD.1  |-  R  e. 
Top
txtopiOLD.2  |-  S  e. 
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Assertion
Ref Expression
txtopiOLD  |-  ( R 
tX  S )  e. 
Top

Proof of Theorem txtopiOLD
StepHypRef Expression
1 txtopiOLD.1 . 2  |-  R  e. 
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2 txtopiOLD.2 . 2  |-  S  e. 
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31, 2txtopi 17117 1  |-  ( R 
tX  S )  e. 
Top
Colors of variables: wff set class
Syntax hints:    e. wcel 1621  (class class class)co 5710   Topctop 16463    tX ctx 17087
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-13 1625  ax-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234  ax-sep 4038  ax-nul 4046  ax-pow 4082  ax-pr 4108  ax-un 4403
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 941  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-eu 2118  df-mo 2119  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ne 2414  df-ral 2513  df-rex 2514  df-rab 2516  df-v 2729  df-sbc 2922  df-csb 3010  df-dif 3081  df-un 3083  df-in 3085  df-ss 3089  df-nul 3363  df-if 3471  df-pw 3532  df-sn 3550  df-pr 3551  df-op 3553  df-uni 3728  df-iun 3805  df-br 3921  df-opab 3975  df-mpt 3976  df-id 4202  df-xp 4594  df-rel 4595  df-cnv 4596  df-co 4597  df-dm 4598  df-rn 4599  df-res 4600  df-ima 4601  df-fun 4602  df-fn 4603  df-f 4604  df-fv 4608  df-ov 5713  df-oprab 5714  df-mpt2 5715  df-1st 5974  df-2nd 5975  df-topgen 13218  df-top 16468  df-bases 16470  df-tx 17089
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