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Theorem intmin4 4080
 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 4068 . . . 4
2 simpr 449 . . . . . . . 8
3 ancr 534 . . . . . . . 8
42, 3impbid2 197 . . . . . . 7
54imbi1d 310 . . . . . 6
65alimi 1569 . . . . 5
7 albi 1574 . . . . 5
86, 7syl 16 . . . 4
91, 8sylbi 189 . . 3
10 vex 2960 . . . 4
1110elintab 4062 . . 3
1210elintab 4062 . . 3
139, 11, 123bitr4g 281 . 2
1413eqrdv 2435 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wal 1550   wceq 1653   wcel 1726  cab 2423   wss 3321  cint 4051 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ral 2711  df-v 2959  df-in 3328  df-ss 3335  df-int 4052
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