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Theorem 2reu5 3317
 Description: Double restricted existential uniqueness in terms of restricted existential quantification and restricted universal quantification, analogous to 2eu5 2392 and reu3 3298. (Contributed by Alexander van der Vekens, 17-Jun-2017.)
Assertion
Ref Expression
2reu5
Distinct variable groups:   ,,,,   ,   ,,,   ,,   ,   ,
Allowed substitution hints:   (,)

Proof of Theorem 2reu5
StepHypRef Expression
1 r19.29r 3003 . . . . . . . 8
2 r19.29r 3003 . . . . . . . . 9
32reximi 2935 . . . . . . . 8
4 pm3.35 587 . . . . . . . . . 10
54reximi 2935 . . . . . . . . 9
65reximi 2935 . . . . . . . 8
7 eleq1 2539 . . . . . . . . . . . . 13
8 eleq1 2539 . . . . . . . . . . . . 13
97, 8bi2anan9 871 . . . . . . . . . . . 12
109biimpac 486 . . . . . . . . . . 11
1110ancomd 451 . . . . . . . . . 10
1211ex 434 . . . . . . . . 9
1312rexlimivv 2964 . . . . . . . 8
141, 3, 6, 134syl 21 . . . . . . 7
1514ex 434 . . . . . 6
1615pm4.71rd 635 . . . . 5
17 anass 649 . . . . 5
1816, 17syl6bb 261 . . . 4
19182exbidv 1692 . . 3
2019pm5.32i 637 . 2
21 2reu5lem3 3316 . 2
22 df-rex 2823 . . . 4
23 r19.42v 3021 . . . . . 6
24 df-rex 2823 . . . . . 6
2523, 24bitr3i 251 . . . . 5
2625exbii 1644 . . . 4
2722, 26bitri 249 . . 3
2827anbi2i 694 . 2
2920, 21, 283bitr4i 277 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369  wex 1596   wcel 1767  wral 2817  wrex 2818  wreu 2819  wrmo 2820 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-eu 2279  df-mo 2280  df-cleq 2459  df-clel 2462  df-ral 2822  df-rex 2823  df-reu 2824  df-rmo 2825 This theorem is referenced by: (None)
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