ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  orduni Unicode version

Theorem orduni 4312
Description: The union of an ordinal class is ordinal. (Contributed by NM, 12-Sep-2003.)
Assertion
Ref Expression
orduni  |-  ( Ord 
A  ->  Ord  U. A
)

Proof of Theorem orduni
StepHypRef Expression
1 ordsson 4309 . 2  |-  ( Ord 
A  ->  A  C_  On )
2 ssorduni 4304 . 2  |-  ( A 
C_  On  ->  Ord  U. A )
31, 2syl 14 1  |-  ( Ord 
A  ->  Ord  U. A
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    C_ wss 2999   U.cuni 3653   Ord word 4189   Oncon0 4190
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-3an 926  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-ral 2364  df-rex 2365  df-v 2621  df-in 3005  df-ss 3012  df-uni 3654  df-tr 3937  df-iord 4193  df-on 4195
This theorem is referenced by:  tfrcl  6129
  Copyright terms: Public domain W3C validator