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Theorem ssint 3776
 Description: Subclass of a class intersection. Theorem 5.11(viii) of [Monk1] p. 52 and its converse. (Contributed by NM, 14-Oct-1999.)
Assertion
Ref Expression
ssint
Distinct variable groups:   ,   ,

Proof of Theorem ssint
StepHypRef Expression
1 dfss3 3093 . 2
2 vex 2730 . . . 4
32elint2 3767 . . 3
43ralbii 2531 . 2
5 ralcom 2662 . . 3
6 dfss3 3093 . . . 4
76ralbii 2531 . . 3
85, 7bitr4i 245 . 2
91, 4, 83bitri 264 1
 Colors of variables: wff set class Syntax hints:   wb 178   wcel 1621  wral 2509   wss 3078  cint 3760 This theorem is referenced by:  ssintab  3777  ssintub  3778  iinpw  3888  trint  4025  oneqmini  4336  fint  5277  sorpssint  6139  iscard2  7493  coftr  7783  isf32lem2  7864  inttsk  8276  isacs1i  13403  mrelatglb  14122  fbfinnfr  17368  fclscmp  17557  dfrtrcl2  23216  fneint  25443  topmeet  25479  igenval2  25857  ismrcd1  25939 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ral 2513  df-v 2729  df-in 3085  df-ss 3089  df-int 3761
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