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Theorem txuniiOLD 26590
Description: The underlying set of the product of two topologies. (Moved to txunii 17304 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
txuniiOLD.1  |-  R  e. 
Top
txuniiOLD.2  |-  S  e. 
Top
txuniiOLD.3  |-  X  = 
U. R
txuniiOLD.4  |-  Y  = 
U. S
Assertion
Ref Expression
txuniiOLD  |-  ( X  X.  Y )  = 
U. ( R  tX  S )

Proof of Theorem txuniiOLD
StepHypRef Expression
1 txuniiOLD.1 . 2  |-  R  e. 
Top
2 txuniiOLD.2 . 2  |-  S  e. 
Top
3 txuniiOLD.3 . 2  |-  X  = 
U. R
4 txuniiOLD.4 . 2  |-  Y  = 
U. S
51, 2, 3, 4txunii 17304 1  |-  ( X  X.  Y )  = 
U. ( R  tX  S )
Colors of variables: wff set class
Syntax hints:    = wceq 1632    e. wcel 1696   U.cuni 3843    X. cxp 4703  (class class class)co 5874   Topctop 16647    tX ctx 17271
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-13 1698  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pow 4204  ax-pr 4230  ax-un 4528
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-sbc 3005  df-csb 3095  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-pw 3640  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-iun 3923  df-br 4040  df-opab 4094  df-mpt 4095  df-id 4325  df-xp 4711  df-rel 4712  df-cnv 4713  df-co 4714  df-dm 4715  df-rn 4716  df-res 4717  df-ima 4718  df-iota 5235  df-fun 5273  df-fn 5274  df-f 5275  df-fv 5279  df-ov 5877  df-oprab 5878  df-mpt2 5879  df-1st 6138  df-2nd 6139  df-topgen 13360  df-top 16652  df-bases 16654  df-topon 16655  df-tx 17273
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