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Theorem trintss 4318
 Description: If is transitive and non-null, then is a subset of . (Contributed by Scott Fenton, 3-Mar-2011.)
Assertion
Ref Expression
trintss

Proof of Theorem trintss
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 vex 2959 . . . 4
21elint2 4057 . . 3
3 r19.2z 3717 . . . . 5
43ex 424 . . . 4
5 trel 4309 . . . . . 6
65exp3acom23 1381 . . . . 5
76rexlimdv 2829 . . . 4
84, 7sylan9 639 . . 3
92, 8syl5bi 209 . 2
109ssrdv 3354 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wcel 1725   wne 2599  wral 2705  wrex 2706   wss 3320  c0 3628  cint 4050   wtr 4302 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 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-v 2958  df-dif 3323  df-in 3327  df-ss 3334  df-nul 3629  df-uni 4016  df-int 4051  df-tr 4303
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