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Theorem dffrege115 36574
 Description: If from the the circumstance that is a result of an application of the procedure to , whatever may be, it can be inferred that every result of an application of the procedure to is the same as , then we say : "The procedure is single-valued". Definition 115 of [Frege1879] p. 77. (Contributed by RP, 7-Jul-2020.)
Assertion
Ref Expression
dffrege115
Distinct variable group:   ,,,

Proof of Theorem dffrege115
StepHypRef Expression
1 alcom 1923 . 2
2 19.21v 1786 . . . . . . 7
3 impexp 448 . . . . . . . . 9
4 vex 3048 . . . . . . . . . . . . 13
5 vex 3048 . . . . . . . . . . . . 13
64, 5brcnv 5017 . . . . . . . . . . . 12
7 df-br 4403 . . . . . . . . . . . 12
85, 4brcnv 5017 . . . . . . . . . . . 12
96, 7, 83bitr3ri 280 . . . . . . . . . . 11
10 vex 3048 . . . . . . . . . . . . 13
114, 10brcnv 5017 . . . . . . . . . . . 12
12 df-br 4403 . . . . . . . . . . . 12
1310, 4brcnv 5017 . . . . . . . . . . . 12
1411, 12, 133bitr3ri 280 . . . . . . . . . . 11
159, 14anbi12ci 704 . . . . . . . . . 10
1615imbi1i 327 . . . . . . . . 9
173, 16bitr3i 255 . . . . . . . 8
1817albii 1691 . . . . . . 7
192, 18bitr3i 255 . . . . . 6
2019albii 1691 . . . . 5
21 alcom 1923 . . . . 5
2220, 21bitri 253 . . . 4
23 opeq2 4167 . . . . . 6
2423eleq1d 2513 . . . . 5
2524mo4 2346 . . . 4
26 mo2v 2306 . . . 4
2722, 25, 263bitr2i 277 . . 3
2827albii 1691 . 2
29 relcnv 5207 . . . 4
3029biantrur 509 . . 3
31 dffun5 5595 . . 3
3230, 31bitr4i 256 . 2
331, 28, 323bitri 275 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 188   wa 371  wal 1442  wex 1663   wcel 1887  wmo 2300  cop 3974   class class class wbr 4402  ccnv 4833   wrel 4839   wfun 5576 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-9 1896  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431  ax-sep 4525  ax-nul 4534  ax-pr 4639 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3an 987  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-eu 2303  df-mo 2304  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-ne 2624  df-ral 2742  df-rex 2743  df-rab 2746  df-v 3047  df-dif 3407  df-un 3409  df-in 3411  df-ss 3418  df-nul 3732  df-if 3882  df-sn 3969  df-pr 3971  df-op 3975  df-br 4403  df-opab 4462  df-id 4749  df-xp 4840  df-rel 4841  df-cnv 4842  df-co 4843  df-fun 5584 This theorem is referenced by:  frege116  36575
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