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Theorem soss 4269
 Description: Subset theorem for the strict ordering predicate. (Contributed by NM, 16-Mar-1997.) (Proof shortened by Andrew Salmon, 25-Jul-2011.)
Assertion
Ref Expression
soss

Proof of Theorem soss
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 poss 4253 . . 3
2 ssel 3118 . . . . . . . 8
3 ssel 3118 . . . . . . . 8
4 ssel 3118 . . . . . . . 8
52, 3, 43anim123d 1298 . . . . . . 7
65imim1d 75 . . . . . 6
762alimdv 1858 . . . . 5
87alimdv 1856 . . . 4
9 r3al 2498 . . . 4
10 r3al 2498 . . . 4
118, 9, 103imtr4g 204 . . 3
121, 11anim12d 333 . 2
13 df-iso 4252 . 2
14 df-iso 4252 . 2
1512, 13, 143imtr4g 204 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wo 698   w3a 963  wal 1330   wcel 2125  wral 2432   wss 3098   class class class wbr 3961   wpo 4249   wor 4250 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-ral 2437  df-in 3104  df-ss 3111  df-po 4251  df-iso 4252 This theorem is referenced by:  soeq2  4271
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