Mathbox for Frédéric Liné < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  mxlelt Unicode version

Theorem mxlelt 25264
 Description: The maximal elements of the preset . (Contributed by FL, 16-May-2011.) (Revised by Mario Carneiro, 11-Sep-2015.)
Hypothesis
Ref Expression
mxlelt.1
Assertion
Ref Expression
mxlelt
Distinct variable groups:   ,,   ,
Allowed substitution hints:   (,)   ()

Proof of Theorem mxlelt
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elex 2796 . 2
2 mxlelt.1 . . . 4
32fldrels 25113 . . 3
4 rabexg 4164 . . 3
53, 4syl 15 . 2
6 unieq 3836 . . . . . 6
76unieqd 3838 . . . . 5
87, 2syl6eqr 2333 . . . 4
98eleq2d 2350 . . . . . 6
10 breq 4025 . . . . . . 7
1110imbi1d 308 . . . . . 6
129, 11imbi12d 311 . . . . 5
1312ralbidv2 2565 . . . 4
148, 13rabeqbidv 2783 . . 3
15 df-mxl 25246 . . 3
1614, 15fvmptg 5600 . 2
171, 5, 16syl2anc 642 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1623   wcel 1684  wral 2543  crab 2547  cvv 2788  cuni 3827   class class class wbr 4023  cfv 5255  cmxl 25216 This theorem is referenced by:  mxlelt2  25265 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-13 1686  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214  ax-un 4512 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-sbc 2992  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-opab 4078  df-mpt 4079  df-id 4309  df-xp 4695  df-rel 4696  df-cnv 4697  df-co 4698  df-dm 4699  df-iota 5219  df-fun 5257  df-fv 5263  df-mxl 25246
 Copyright terms: Public domain W3C validator