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Theorem eqint 25063
 Description: To prove that a set is the finest one that has the property , prove that is a part of all sets that has this property and that has also that property. (Contributed by FL, 21-Apr-2012.)
Hypotheses
Ref Expression
eqint.1
eqint.2
eqint.3
Assertion
Ref Expression
eqint
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem eqint
StepHypRef Expression
1 ssintab 3895 . . . 4
2 eqint.3 . . . 4
31, 2mpgbir 1540 . . 3
43a1i 10 . 2
5 eqint.1 . . 3
6 eqint.2 . . 3
75, 6intmin3 3906 . 2
84, 7eqssd 3209 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wceq 1632   wcel 1696  cab 2282   wss 3165  cint 3878 This theorem is referenced by:  intopcoaconb  25643 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-v 2803  df-in 3172  df-ss 3179  df-int 3879
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