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Theorem puub2 25361
 Description: The predicate " is an upper bound of ." (Contributed by FL, 16-May-2011.)
Hypothesis
Ref Expression
puub2.1
Assertion
Ref Expression
puub2 PresetRel
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem puub2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 puub2.1 . . . 4
21ubos2 25360 . . 3 PresetRel
32eleq2d 2363 . 2 PresetRel
4 breq2 4043 . . . 4
54ralbidv 2576 . . 3
65elrab 2936 . 2
73, 6syl6bb 252 1 PresetRel
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358   wceq 1632   wcel 1696  wral 2556  crab 2560   class class class wbr 4039   cdm 4705  (class class class)co 5874  PresetRelcpresetrel 25318   cub 25321 This theorem is referenced by:  prltub  25363  ubpar  25364  supaub  25376  supwlub  25377 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-13 1698  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230  ax-un 4528 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-sbc 3005  df-csb 3095  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-pw 3640  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-iun 3923  df-br 4040  df-opab 4094  df-id 4325  df-xp 4711  df-rel 4712  df-cnv 4713  df-co 4714  df-dm 4715  df-rn 4716  df-res 4717  df-iota 5235  df-fun 5273  df-fv 5279  df-ov 5877  df-oprab 5878  df-mpt2 5879  df-prs 25326  df-ub 25356
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