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Theorem srefwref 25170
 Description: Strong reflexivity implies weak reflexivity. (Strong and weak reflexivity is the difference between a toset and a poset). (Contributed by FL, 29-Dec-2011.)
Assertion
Ref Expression
srefwref
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem srefwref
StepHypRef Expression
1 breq2 4043 . . . . 5
2 breq1 4042 . . . . 5
31, 2orbi12d 690 . . . 4
43rspcva 2895 . . 3
5 pm4.25 501 . . 3
64, 5sylibr 203 . 2
76ralimiaa 2630 1
 Colors of variables: wff set class Syntax hints:   wi 4   wo 357   wa 358   wcel 1696  wral 2556   cun 3163   class class class wbr 4039   cdm 4705   crn 4706 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-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 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-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-br 4040
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