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Theorem ssunieq 3641
 Description: Relationship implying union. (Contributed by NM, 10-Nov-1999.)
Assertion
Ref Expression
ssunieq
Distinct variable groups:   ,   ,

Proof of Theorem ssunieq
StepHypRef Expression
1 elssuni 3636 . . 3
2 unissb 3638 . . . 4
32biimpri 128 . . 3
41, 3anim12i 325 . 2
5 eqss 2988 . 2
64, 5sylibr 141 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101   wceq 1259   wcel 1409  wral 2323   wss 2945  cuni 3608 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328  df-v 2576  df-in 2952  df-ss 2959  df-uni 3609 This theorem is referenced by:  unimax  3642
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