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Theorem isbasisg 16517
 Description: Express the predicate " is a basis for a topology." (Contributed by NM, 17-Jul-2006.)
Assertion
Ref Expression
isbasisg
Distinct variable group:   ,,
Allowed substitution hints:   (,)

Proof of Theorem isbasisg
StepHypRef Expression
1 ineq1 3271 . . . . . 6
21unieqd 3738 . . . . 5
32sseq2d 3127 . . . 4
43raleqbi1dv 2696 . . 3
54raleqbi1dv 2696 . 2
6 df-bases 16470 . 2
75, 6elab2g 2853 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wceq 1619   wcel 1621  wral 2509   cin 3077   wss 3078  cpw 3530  cuni 3727  ctb 16467 This theorem is referenced by:  isbasis2g  16518  basis1  16520  basdif0  16523  baspartn  16524  basqtop  17234 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-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ral 2513  df-rex 2514  df-v 2729  df-in 3085  df-ss 3089  df-uni 3728  df-bases 16470
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