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Theorem trintss 4513
 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 3048 . . . 4
21elint2 4241 . . 3
3 r19.2z 3858 . . . . 5
43ex 436 . . . 4
5 trel 4504 . . . . . 6
65expcomd 440 . . . . 5
76rexlimdv 2877 . . . 4
84, 7sylan9 663 . . 3
92, 8syl5bi 221 . 2
109ssrdv 3438 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 371   wcel 1887   wne 2622  wral 2737  wrex 2738   wss 3404  c0 3731  cint 4234   wtr 4497 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-ne 2624  df-ral 2742  df-rex 2743  df-v 3047  df-dif 3407  df-in 3411  df-ss 3418  df-nul 3732  df-uni 4199  df-int 4235  df-tr 4498 This theorem is referenced by: (None)
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