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Theorem frss 4851
Description: Subset theorem for the well-founded predicate. Exercise 1 of [TakeutiZaring] p. 31. (Contributed by NM, 3-Apr-1994.) (Proof shortened by Andrew Salmon, 25-Jul-2011.)
Assertion
Ref Expression
frss

Proof of Theorem frss
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 sstr2 3510 . . . . . 6
21com12 31 . . . . 5
32anim1d 564 . . . 4
43imim1d 75 . . 3
54alimdv 1709 . 2
6 df-fr 4843 . 2
7 df-fr 4843 . 2
85, 6, 73imtr4g 270 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  /\wa 369  A.wal 1393  =/=wne 2652  A.wral 2807  E.wrex 2808  C_wss 3475   c0 3784   class class class wbr 4452  Frwfr 4840
This theorem is referenced by:  freq2  4855  wess  4871  frmin  29322  frrlem5  29391
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-in 3482  df-ss 3489  df-fr 4843
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