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Theorem poss 4497
 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 3399 . . 3
2 ssralv 3399 . . . . 5
3 ssralv 3399 . . . . . 6
43ralimdv 2777 . . . . 5
52, 4syld 42 . . . 4
65ralimdv 2777 . . 3
71, 6syld 42 . 2
8 df-po 4495 . 2
9 df-po 4495 . 2
107, 8, 93imtr4g 262 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359  wral 2697   wss 3312   class class class wbr 4204   wpo 4493 This theorem is referenced by:  poeq2  4499  soss  4513  swoso  6928  frfi  7344  wemapso2lem  7509  fin23lem27  8198  zorn2lem6  8371  xrge0iifiso  24311  incsequz2  26407 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-ral 2702  df-in 3319  df-ss 3326  df-po 4495
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