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Theorem reuss2 3535
 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 2620 . . 3
2 df-reu 2621 . . 3
31, 2anbi12i 678 . 2
4 df-ral 2619 . . . . . . 7
5 ssel 3267 . . . . . . . . . . . . . 14
6 prth 554 . . . . . . . . . . . . . 14
75, 6sylan 457 . . . . . . . . . . . . 13
87exp4b 590 . . . . . . . . . . . 12
98com23 72 . . . . . . . . . . 11
109a2d 23 . . . . . . . . . 10
1110imp4a 572 . . . . . . . . 9
1211alimdv 1621 . . . . . . . 8
1312imp 418 . . . . . . 7
144, 13sylan2b 461 . . . . . 6
15 euimmo 2253 . . . . . 6
1614, 15syl 15 . . . . 5
17 eu5 2242 . . . . . 6
1817simplbi2 608 . . . . 5
1916, 18syl9 66 . . . 4
2019imp32 422 . . 3
21 df-reu 2621 . . 3
2220, 21sylibr 203 . 2
233, 22sylan2b 461 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 358  wal 1540  wex 1541   wcel 1710  weu 2204  wmo 2205  wral 2614  wrex 2615  wreu 2616   wss 3257 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-rex 2620  df-reu 2621  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259 This theorem is referenced by:  reuss  3536  reuun1  3537
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