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Theorem dffrege99 36528
 Description: If is identical with or follows in the -sequence, then we say : " belongs to the -sequence beginning with " or " belongs to the -sequence ending with ". Definition 99 of [Frege1879] p. 71. (Contributed by RP, 2-Jul-2020.)
Hypothesis
Ref Expression
frege99.z
Assertion
Ref Expression
dffrege99

Proof of Theorem dffrege99
StepHypRef Expression
1 brun 4472 . 2
2 df-or 371 . 2
3 frege99.z . . . . . 6
43elexi 3090 . . . . 5
54ideq 5006 . . . 4
6 eqcom 2431 . . . 4
75, 6bitri 252 . . 3
87imbi2i 313 . 2
91, 2, 83bitrri 275 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 187   wo 369   wceq 1437   wcel 1872   cun 3434   class class class wbr 4423   cid 4763  cfv 5601  ctcl 13049 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-9 1876  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401  ax-sep 4546  ax-nul 4555  ax-pr 4660 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-eu 2273  df-mo 2274  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-ne 2616  df-ral 2776  df-rex 2777  df-rab 2780  df-v 3082  df-dif 3439  df-un 3441  df-in 3443  df-ss 3450  df-nul 3762  df-if 3912  df-sn 3999  df-pr 4001  df-op 4005  df-br 4424  df-opab 4483  df-id 4768  df-xp 4859  df-rel 4860 This theorem is referenced by:  frege100  36529  frege105  36534
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