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Theorem isbasisg 17012
 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
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ineq1 3535 . . . . . 6
21unieqd 4026 . . . . 5
32sseq2d 3376 . . . 4
43raleqbi1dv 2912 . . 3
54raleqbi1dv 2912 . 2
6 df-bases 16965 . 2
75, 6elab2g 3084 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wceq 1652   wcel 1725  wral 2705   cin 3319   wss 3320  cpw 3799  cuni 4015  ctb 16962 This theorem is referenced by:  isbasis2g  17013  basis1  17015  basdif0  17018  baspartn  17019  basqtop  17743 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 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-v 2958  df-in 3327  df-ss 3334  df-uni 4016  df-bases 16965
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