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Theorem unidif 3875
 Description: If the difference contains the largest members of , then the union of the difference is the union of . (Contributed by NM, 22-Mar-2004.)
Assertion
Ref Expression
unidif
Distinct variable groups:   ,,   ,,

Proof of Theorem unidif
StepHypRef Expression
1 uniss2 3874 . . 3
2 difss 3316 . . . 4
3 uniss 3864 . . . 4
42, 3ax-mp 8 . . 3
51, 4jctil 523 . 2
6 eqss 3207 . 2
75, 6sylibr 203 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358   wceq 1632  wral 2556  wrex 2557   cdif 3162   wss 3165  cuni 3843 This theorem is referenced by:  ordunidif  4456 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-rex 2562  df-v 2803  df-dif 3168  df-in 3172  df-ss 3179  df-uni 3844
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