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Theorem inttpemp 25139
 Description: Two ways of saying that two triples have no common element. (Contributed by FL, 29-May-2014.) (Proof shortened by Mario Carneiro, 26-Apr-2015.)
Assertion
Ref Expression
inttpemp

Proof of Theorem inttpemp
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 disj 3495 . 2
2 eleq1 2343 . . . . . 6
3 id 19 . . . . . . . 8
4 vex 2791 . . . . . . . 8
53, 4syl6eqelr 2372 . . . . . . 7
6 eltpg 3676 . . . . . . 7
75, 6syl 15 . . . . . 6
82, 7bitrd 244 . . . . 5
98notbid 285 . . . 4
10 ne3anior 2532 . . . 4
119, 10syl6bbr 254 . . 3
12 eleq1 2343 . . . . . 6
13 id 19 . . . . . . . 8
1413, 4syl6eqelr 2372 . . . . . . 7
15 eltpg 3676 . . . . . . 7
1614, 15syl 15 . . . . . 6
1712, 16bitrd 244 . . . . 5
1817notbid 285 . . . 4
19 ne3anior 2532 . . . 4
2018, 19syl6bbr 254 . . 3
21 eleq1 2343 . . . . . 6
22 id 19 . . . . . . . 8
2322, 4syl6eqelr 2372 . . . . . . 7
24 eltpg 3676 . . . . . . 7
2523, 24syl 15 . . . . . 6
2621, 25bitrd 244 . . . . 5
2726notbid 285 . . . 4
28 ne3anior 2532 . . . 4
2927, 28syl6bbr 254 . . 3
3011, 20, 29raltpg 3684 . 2
311, 30syl5bb 248 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 176   w3o 933   w3a 934   wceq 1623   wcel 1684   wne 2446  wral 2543  cvv 2788   cin 3151  c0 3455  ctp 3642 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3or 935  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-v 2790  df-sbc 2992  df-dif 3155  df-un 3157  df-in 3159  df-nul 3456  df-sn 3646  df-pr 3647  df-tp 3648
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