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Theorem intprg 3960
 Description: The intersection of a pair is the intersection of its members. Closed form of intpr 3959. Theorem 71 of [Suppes] p. 42. (Contributed by FL, 27-Apr-2008.)
Assertion
Ref Expression
intprg

Proof of Theorem intprg
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 preq1 3799 . . . 4
21inteqd 3931 . . 3
3 ineq1 3450 . . 3
42, 3eqeq12d 2367 . 2
5 preq2 3800 . . . 4
65inteqd 3931 . . 3
7 ineq2 3451 . . 3
86, 7eqeq12d 2367 . 2
9 vex 2862 . . 3
10 vex 2862 . . 3
119, 10intpr 3959 . 2
124, 8, 11vtocl2g 2918 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 358   wceq 1642   wcel 1710   cin 3208  cpr 3738  cint 3926 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-sn 3741  df-pr 3742  df-int 3927 This theorem is referenced by:  intsng  3961
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