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Theorem isbasis3g 17002
 Description: Express the predicate " is a basis for a topology." Definition of basis in [Munkres] p. 78. (Contributed by NM, 17-Jul-2006.)
Assertion
Ref Expression
isbasis3g
Distinct variable group:   ,,,,
Allowed substitution hints:   (,,,)

Proof of Theorem isbasis3g
StepHypRef Expression
1 isbasis2g 17001 . 2
2 elssuni 4035 . . . . . 6
32rgen 2763 . . . . 5
4 eluni2 4011 . . . . . . 7
54biimpi 187 . . . . . 6
65rgen 2763 . . . . 5
73, 6pm3.2i 442 . . . 4
87biantrur 493 . . 3
9 df-3an 938 . . 3
108, 9bitr4i 244 . 2
111, 10syl6bb 253 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   w3a 936   wcel 1725  wral 2697  wrex 2698   cin 3311   wss 3312  cuni 4007  ctb 16950 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 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-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-v 2950  df-in 3319  df-ss 3326  df-pw 3793  df-uni 4008  df-bases 16953
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