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Theorem uniss 3564
Description: Subclass relationship for class union. Theorem 61 of [Suppes] p. 39. (Contributed by NM, 22-Mar-1998.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)
Assertion
Ref Expression
uniss 
C_  U.  C_  U.

Proof of Theorem uniss
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ssel 2907 . . . . 5 
C_
21anim2d 320 . . . 4 
C_
32eximdv 1733 . . 3 
C_
4 eluni 3546 . . 3  U.
5 eluni 3546 . . 3  U.
63, 4, 53imtr4g 194 . 2 
C_  U.  U.
76ssrdv 2919 1 
C_  U.  C_  U.
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97  wex 1354   wcel 1366    C_ wss 2885   U.cuni 3543
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 614  ax-5 1309  ax-7 1310  ax-gen 1311  ax-ie1 1355  ax-ie2 1356  ax-8 1368  ax-10 1369  ax-11 1370  ax-i12 1371  ax-bnd 1372  ax-4 1373  ax-17 1392  ax-i9 1396  ax-ial 1400  ax-i5r 1401  ax-ext 1995
This theorem depends on definitions:  df-bi 110  df-tru 1226  df-nf 1323  df-sb 1619  df-clab 2000  df-cleq 2006  df-clel 2009  df-nfc 2140  df-v 2528  df-in 2892  df-ss 2899  df-uni 3544
This theorem is referenced by:  unissi  3566  unissd  3567  intssuni2m  3602  relfld  4761
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