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Theorem reuss2 3777
Description: Transfer uniqueness to a smaller subclass. (Contributed by NM, 20-Oct-2005.)
Assertion
Ref Expression
reuss2
Distinct variable groups:   ,   ,

Proof of Theorem reuss2
StepHypRef Expression
1 df-rex 2813 . . 3
2 df-reu 2814 . . 3
31, 2anbi12i 697 . 2
4 df-ral 2812 . . . . . . 7
5 ssel 3497 . . . . . . . . . . . . . 14
6 prth 571 . . . . . . . . . . . . . 14
75, 6sylan 471 . . . . . . . . . . . . 13
87exp4b 607 . . . . . . . . . . . 12
98com23 78 . . . . . . . . . . 11
109a2d 26 . . . . . . . . . 10
1110imp4a 589 . . . . . . . . 9
1211alimdv 1709 . . . . . . . 8
1312imp 429 . . . . . . 7
144, 13sylan2b 475 . . . . . 6
15 euimmo 2343 . . . . . 6
1614, 15syl 16 . . . . 5
17 eu5 2310 . . . . . 6
1817simplbi2 625 . . . . 5
1916, 18syl9 71 . . . 4
2019imp32 433 . . 3
21 df-reu 2814 . . 3
2220, 21sylibr 212 . 2
233, 22sylan2b 475 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  A.wal 1393  E.wex 1612  e.wcel 1818  E!weu 2282  E*wmo 2283  A.wral 2807  E.wrex 2808  E!wreu 2809  C_wss 3475
This theorem is referenced by:  reuss  3778  reuun1  3779  riotass2  6284
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-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-ral 2812  df-rex 2813  df-reu 2814  df-in 3482  df-ss 3489
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