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Theorem poss 4792
 Description: Subset theorem for the partial ordering predicate. (Contributed by NM, 27-Mar-1997.) (Proof shortened by Mario Carneiro, 18-Nov-2016.)
Assertion
Ref Expression
poss

Proof of Theorem poss
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ssralv 3549 . . 3
2 ssralv 3549 . . . . 5
3 ssralv 3549 . . . . . 6
43ralimdv 2853 . . . . 5
52, 4syld 44 . . . 4
65ralimdv 2853 . . 3
71, 6syld 44 . 2
8 df-po 4790 . 2
9 df-po 4790 . 2
107, 8, 93imtr4g 270 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 369  wral 2793   wss 3461   class class class wbr 4437   wpo 4788 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-ral 2798  df-in 3468  df-ss 3475  df-po 4790 This theorem is referenced by:  poeq2  4794  soss  4808  swoso  7344  frfi  7767  wemapsolem  7978  fin23lem27  8711  zorn2lem6  8884  xrge0iifiso  27790  incsequz2  30217
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