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Theorem intmin4 4316
 Description: Elimination of a conjunct in a class intersection. (Contributed by NM, 31-Jul-2006.)
Assertion
Ref Expression
intmin4
Distinct variable group:   ,

Proof of Theorem intmin4
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ssintab 4303 . . . 4
2 simpr 461 . . . . . . . 8
3 ancr 549 . . . . . . . 8
42, 3impbid2 204 . . . . . . 7
54imbi1d 317 . . . . . 6
65alimi 1633 . . . . 5
7 albi 1639 . . . . 5
86, 7syl 16 . . . 4
91, 8sylbi 195 . . 3
10 vex 3112 . . . 4
1110elintab 4297 . . 3
1210elintab 4297 . . 3
139, 11, 123bitr4g 288 . 2
1413eqrdv 2454 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  e.wcel 1818  {cab 2442  C_wss 3475  |^|cint 4286 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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 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-ral 2812  df-v 3111  df-in 3482  df-ss 3489  df-int 4287
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