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Theorem 2reu5 3044
Description: Double restricted existential uniqueness in terms of restricted existential quantification and restricted universal quantification, analogous to 2eu5 2288 and reu3 3026. (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 2755 . . . . . . . 8
2 r19.29r 2755 . . . . . . . . 9
32reximi 2721 . . . . . . . 8
4 pm3.35 570 . . . . . . . . . . 11
54reximi 2721 . . . . . . . . . 10
65reximi 2721 . . . . . . . . 9
7 eleq1 2413 . . . . . . . . . . . . . 14
8 eleq1 2413 . . . . . . . . . . . . . 14
97, 8bi2anan9 843 . . . . . . . . . . . . 13
109biimpac 472 . . . . . . . . . . . 12
1110ancomd 438 . . . . . . . . . . 11
1211ex 423 . . . . . . . . . 10
1312rexlimivv 2743 . . . . . . . . 9
146, 13syl 15 . . . . . . . 8
151, 3, 143syl 18 . . . . . . 7
1615ex 423 . . . . . 6
1716pm4.71rd 616 . . . . 5
18 anass 630 . . . . 5
1917, 18syl6bb 252 . . . 4
20192exbidv 1628 . . 3
2120pm5.32i 618 . 2
22 2reu5lem3 3043 . 2
23 df-rex 2620 . . . 4
24 r19.42v 2765 . . . . . 6
25 df-rex 2620 . . . . . 6
2624, 25bitr3i 242 . . . . 5
2726exbii 1582 . . . 4
2823, 27bitri 240 . . 3
2928anbi2i 675 . 2
3021, 22, 293bitr4i 268 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wb 176   wa 358  wex 1541   wcel 1710  wral 2614  wrex 2615  wreu 2616  wrmo 2617
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209  df-cleq 2346  df-clel 2349  df-ral 2619  df-rex 2620  df-reu 2621  df-rmo 2622
This theorem is referenced by: (None)
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