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Theorem unidif 4234
 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 4233 . . 3
2 difss 3562 . . . 4
32unissi 4224 . . 3
41, 3jctil 540 . 2
5 eqss 3449 . 2
64, 5sylibr 216 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 371   wceq 1446  wral 2739  wrex 2740   cdif 3403   wss 3406  cuni 4201 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1671  ax-4 1684  ax-5 1760  ax-6 1807  ax-7 1853  ax-10 1917  ax-11 1922  ax-12 1935  ax-13 2093  ax-ext 2433 This theorem depends on definitions:  df-bi 189  df-an 373  df-tru 1449  df-ex 1666  df-nf 1670  df-sb 1800  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2583  df-ral 2744  df-rex 2745  df-v 3049  df-dif 3409  df-in 3413  df-ss 3420  df-uni 4202 This theorem is referenced by:  ordunidif  5474
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