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Theorem reu3 3289
Description: A way to express restricted uniqueness. (Contributed by NM, 24-Oct-2006.)
Assertion
Ref Expression
reu3
Distinct variable groups:   , ,   ,

Proof of Theorem reu3
StepHypRef Expression
1 reurex 3074 . . 3
2 reu6 3288 . . . 4
3 bi1 186 . . . . . 6
43ralimi 2850 . . . . 5
54reximi 2925 . . . 4
62, 5sylbi 195 . . 3
71, 6jca 532 . 2
8 rexex 2914 . . . 4
98anim2i 569 . . 3
10 eu3v 2312 . . . 4
11 df-reu 2814 . . . 4
12 df-rex 2813 . . . . 5
13 df-ral 2812 . . . . . . 7
14 impexp 446 . . . . . . . 8
1514albii 1640 . . . . . . 7
1613, 15bitr4i 252 . . . . . 6
1716exbii 1667 . . . . 5
1812, 17anbi12i 697 . . . 4
1910, 11, 183bitr4i 277 . . 3
209, 19sylibr 212 . 2
217, 20impbii 188 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  E.wex 1612  e.wcel 1818  E!weu 2282  A.wral 2807  E.wrex 2808  E!wreu 2809
This theorem is referenced by:  reu7  3294  2reu4a  32194
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-cleq 2449  df-clel 2452  df-ral 2812  df-rex 2813  df-reu 2814  df-rmo 2815
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