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Theorem istpsOLD 16985
 Description: Express the predicate "is a topological space." (Contributed by NM, 18-Jul-2006.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
istpsOLD

Proof of Theorem istpsOLD
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 tpsexOLD 16984 . 2
2 simpr 448 . . . 4
3 uniexg 4706 . . . . 5
43adantr 452 . . . 4
52, 4eqeltrd 2510 . . 3
6 elex 2964 . . . 4
85, 7jca 519 . 2
9 df-topspOLD 16964 . . . 4
109eleq2i 2500 . . 3
11 eqeq1 2442 . . . . 5
1211anbi2d 685 . . . 4
13 eleq1 2496 . . . . 5
14 unieq 4024 . . . . . 6
1514eqeq2d 2447 . . . . 5
1613, 15anbi12d 692 . . . 4
1712, 16opelopabg 4473 . . 3
1810, 17syl5bb 249 . 2
191, 8, 18pm5.21nii 343 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359   wceq 1652   wcel 1725  cvv 2956  cop 3817  cuni 4015  copab 4265  ctop 16958  ctpsOLD 16960 This theorem is referenced by:  istps2OLD  16986  retpsOLD  18798 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403  ax-un 4701 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-opab 4267  df-xp 4884  df-rel 4885  df-topspOLD 16964
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