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Theorem txtopiOLD 25853
Description: The product of two topologies is a topology. (Moved to txtopi 17247 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. 
Top
Assertion
Ref Expression
txtopiOLD  |-  ( R 
tX  S )  e. 
Top

Proof of Theorem txtopiOLD
StepHypRef Expression
1 txtopiOLD.1 . 2  |-  R  e. 
Top
2 txtopiOLD.2 . 2  |-  S  e. 
Top
31, 2txtopi 17247 1  |-  ( R 
tX  S )  e. 
Top
Colors of variables: wff set class
Syntax hints:    e. wcel 1621  (class class class)co 5792   Topctop 16593    tX ctx 17217
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 1927  ax-ext 2239  ax-sep 4115  ax-nul 4123  ax-pow 4160  ax-pr 4186  ax-un 4484
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 1884  df-eu 2122  df-mo 2123  df-clab 2245  df-cleq 2251  df-clel 2254  df-nfc 2383  df-ne 2423  df-ral 2523  df-rex 2524  df-rab 2527  df-v 2765  df-sbc 2967  df-csb 3057  df-dif 3130  df-un 3132  df-in 3134  df-ss 3141  df-nul 3431  df-if 3540  df-pw 3601  df-sn 3620  df-pr 3621  df-op 3623  df-uni 3802  df-iun 3881  df-br 3998  df-opab 4052  df-mpt 4053  df-id 4281  df-xp 4675  df-rel 4676  df-cnv 4677  df-co 4678  df-dm 4679  df-rn 4680  df-res 4681  df-ima 4682  df-fun 4683  df-fn 4684  df-f 4685  df-fv 4689  df-ov 5795  df-oprab 5796  df-mpt2 5797  df-1st 6056  df-2nd 6057  df-topgen 13306  df-top 16598  df-bases 16600  df-tx 17219
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