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Theorem inposetlem 25379
 Description: Lemma for inposet 25381. Definition of inclusion of sets using a class. (Contributed by FL, 22-Sep-2008.)
Hypotheses
Ref Expression
inposetlem.1
inposetlem.2
inposetlem.3
Assertion
Ref Expression
inposetlem
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem inposetlem
StepHypRef Expression
1 inposetlem.1 . 2
2 inposetlem.2 . 2
3 sseq1 3212 . 2
4 sseq2 3213 . 2
5 inposetlem.3 . 2
61, 2, 3, 4, 5brab 4303 1
 Colors of variables: wff set class Syntax hints:   wb 176   wceq 1632   wcel 1696  cvv 2801   wss 3165   class class class wbr 4039  copab 4092 This theorem is referenced by:  inposet  25381  definc  25382 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-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 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-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  df-opab 4094
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