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Theorem intmin4 3643
 Description: Elimination of a conjunct in a class intersection. (Contributed by NM, 31-Jul-2006.)
Assertion
Ref Expression
intmin4
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem intmin4
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ssintab 3632 . . . 4
2 simpr 103 . . . . . . . 8
3 ancr 304 . . . . . . . 8
42, 3impbid2 131 . . . . . . 7
54imbi1d 220 . . . . . 6
65alimi 1344 . . . . 5
7 albi 1357 . . . . 5
86, 7syl 14 . . . 4
91, 8sylbi 114 . . 3
10 vex 2560 . . . 4
1110elintab 3626 . . 3
1210elintab 3626 . . 3
139, 11, 123bitr4g 212 . 2
1413eqrdv 2038 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98  wal 1241   wceq 1243   wcel 1393  cab 2026   wss 2917  cint 3615 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-v 2559  df-in 2924  df-ss 2931  df-int 3616 This theorem is referenced by: (None)
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