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Theorem intabs 4613
 Description: Absorption of a redundant conjunct in the intersection of a class abstraction. (Contributed by NM, 3-Jul-2005.)
Hypotheses
Ref Expression
intabs.1
intabs.2
intabs.3
Assertion
Ref Expression
intabs
Distinct variable groups:   ,   ,   ,   ,   ,

Proof of Theorem intabs
StepHypRef Expression
1 sseq1 3524 . . . . . 6
2 intabs.2 . . . . . 6
31, 2anbi12d 710 . . . . 5
4 intabs.3 . . . . 5
53, 4intmin3 4315 . . . 4
6 intnex 4609 . . . . 5
7 ssv 3523 . . . . . 6
8 sseq2 3525 . . . . . 6
97, 8mpbiri 233 . . . . 5
106, 9sylbi 195 . . . 4
115, 10pm2.61i 164 . . 3
12 intabs.1 . . . . 5
1312cbvabv 2600 . . . 4
1413inteqi 4290 . . 3
1511, 14sseqtr4i 3536 . 2
16 simpr 461 . . . 4
1716ss2abi 3571 . . 3
18 intss 4307 . . 3
1917, 18ax-mp 5 . 2
2015, 19eqssi 3519 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  {cab 2442   cvv 3109  C_wss 3475  |^|cint 4286 This theorem is referenced by:  dfnn3  10575 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-8 1820  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-v 3111  df-dif 3478  df-in 3482  df-ss 3489  df-nul 3785  df-int 4287
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