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Theorem sstr2 3279
 Description: Transitivity of subclasses. Exercise 5 of [TakeutiZaring] p. 17. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)
Assertion
Ref Expression
sstr2

Proof of Theorem sstr2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ssel 3267 . . . 4
21imim1d 69 . . 3
32alimdv 1621 . 2
4 dfss2 3262 . 2
5 dfss2 3262 . 2
63, 4, 53imtr4g 261 1
 Colors of variables: wff setvar class Syntax hints:   wi 4  wal 1540   wcel 1710   wss 3257 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259 This theorem is referenced by:  sstr  3280  sstri  3281  sseq1  3292  sseq2  3293  ssun3  3428  ssun4  3429  ssinss1  3483  ssdisj  3600  sspwb  4118  funss  5126  funimass2  5170  fss  5230
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