Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  reuss2 Structured version   Unicode version

Theorem reuss2 3783
 Description: Transfer uniqueness to a smaller subclass. (Contributed by NM, 20-Oct-2005.)
Assertion
Ref Expression
reuss2
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem reuss2
StepHypRef Expression
1 df-rex 2823 . . 3
2 df-reu 2824 . . 3
31, 2anbi12i 697 . 2
4 df-ral 2822 . . . . . . 7
5 ssel 3503 . . . . . . . . . . . . . 14
6 prth 571 . . . . . . . . . . . . . 14
75, 6sylan 471 . . . . . . . . . . . . 13
87exp4b 607 . . . . . . . . . . . 12
98com23 78 . . . . . . . . . . 11
109a2d 26 . . . . . . . . . 10
1110imp4a 589 . . . . . . . . 9
1211alimdv 1685 . . . . . . . 8
1312imp 429 . . . . . . 7
144, 13sylan2b 475 . . . . . 6
15 euimmo 2345 . . . . . 6
1614, 15syl 16 . . . . 5
17 eu5 2305 . . . . . 6
1817simplbi2 625 . . . . 5
1916, 18syl9 71 . . . 4
2019imp32 433 . . 3
21 df-reu 2824 . . 3
2220, 21sylibr 212 . 2
233, 22sylan2b 475 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369  wal 1377  wex 1596   wcel 1767  weu 2275  wmo 2276  wral 2817  wrex 2818  wreu 2819   wss 3481 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-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-ral 2822  df-rex 2823  df-reu 2824  df-in 3488  df-ss 3495 This theorem is referenced by:  reuss  3784  reuun1  3785  riotass2  6283
 Copyright terms: Public domain W3C validator