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Theorem indistps2ALT 17070
 Description: The indiscrete topology on a set expressed as a topological space, using direct component assignments. Here we show how to derive the direct component assignment version indistps2 17068 from the structural version indistps 17067. (Contributed by NM, 24-Oct-2012.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
indistps2ALT.a
indistps2ALT.j
Assertion
Ref Expression
indistps2ALT

Proof of Theorem indistps2ALT
StepHypRef Expression
1 indistps2ALT.a . . . 4
2 fvex 5734 . . . 4
31, 2eqeltrri 2506 . . 3
4 indistopon 17057 . . 3 TopOn
53, 4ax-mp 8 . 2 TopOn
61eqcomi 2439 . . 3
7 indistps2ALT.j . . . 4
87eqcomi 2439 . . 3
96, 8istps 16993 . 2 TopOn
105, 9mpbir 201 1
 Colors of variables: wff set class Syntax hints:   wceq 1652   wcel 1725  cvv 2948  c0 3620  cpr 3807  cfv 5446  cbs 13461  ctopn 13641  TopOnctopon 16951  ctps 16953 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 2416  ax-sep 4322  ax-nul 4330  ax-pow 4369  ax-pr 4395  ax-un 4693 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 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-pw 3793  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-mpt 4260  df-id 4490  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-iota 5410  df-fun 5448  df-fv 5454  df-top 16955  df-topon 16958  df-topsp 16959
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