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Theorem kqfeq 17757
 Description: Two points in the Kolmogorov quotient are equal iff the original points are topologically indistinguishable. (Contributed by Mario Carneiro, 25-Aug-2015.)
Hypothesis
Ref Expression
kqval.2
Assertion
Ref Expression
kqfeq
Distinct variable groups:   ,,   ,,   ,,   ,,   ,
Allowed substitution hints:   (,)   ()

Proof of Theorem kqfeq
StepHypRef Expression
1 kqval.2 . . . . 5
21kqfval 17756 . . . 4
41kqfval 17756 . . . 4
63, 5eqeq12d 2451 . 2
7 rabbi 2887 . 2
86, 7syl6bbr 256 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   w3a 937   wceq 1653   wcel 1726  wral 2706  crab 2710   cmpt 4267  cfv 5455 This theorem is referenced by:  ist0-4  17762  kqfvima  17763  kqt0lem  17769  isr0  17770  r0cld  17771  regr1lem2  17773 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418  ax-sep 4331  ax-nul 4339  ax-pr 4404 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2286  df-mo 2287  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ne 2602  df-ral 2711  df-rex 2712  df-rab 2715  df-v 2959  df-sbc 3163  df-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-nul 3630  df-if 3741  df-sn 3821  df-pr 3822  df-op 3824  df-uni 4017  df-br 4214  df-opab 4268  df-mpt 4269  df-id 4499  df-xp 4885  df-rel 4886  df-cnv 4887  df-co 4888  df-dm 4889  df-iota 5419  df-fun 5457  df-fv 5463
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