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Theorem splintx 25049
 Description: Moving an element out from an intersection. (Contributed by FL, 15-Oct-2012.)
Hypothesis
Ref Expression
splintx.1
Assertion
Ref Expression
splintx
Distinct variable groups:   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem splintx
StepHypRef Expression
1 snssi 3759 . . 3
2 splint 25048 . . 3
31, 2syl 15 . 2
4 splintx.1 . . . 4
54iinxsng 3978 . . 3
65ineq2d 3370 . 2
73, 6eqtrd 2315 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1623   wcel 1684   cdif 3149   cin 3151   wss 3152  csn 3640  ciin 3906 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-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-rab 2552  df-v 2790  df-sbc 2992  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-sn 3646  df-iin 3908
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