Theorem limuni2 3030

Description: The union of a limit ordinal is a limit ordinal.

Assertion

Ref	Expression
limuni2	|- (Lim A -> Lim U.A)

Proof of Theorem limuni2

Step	Hyp	Ref	Expression
1		limuni 3029	. . 3 |- (Lim A -> A = U.A)
2		limeq 2960	. . 3 |- (A = U.A -> (Lim A <-> Lim U.A))
3	1, 2	syl 10	. 2 |- (Lim A -> (Lim A <-> Lim U.A))
4	3	ibi 592	1 |- (Lim A -> Lim U.A)

Syntax hints:   -> wi 3   <-> wb 146   = wceq 956  U.cuni 2503  Lim wlim 2949

This theorem is referenced by:  rankxplim2 4713  rankxplim3 4714

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-3an 777  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-ne 1587  df-ral 1649  df-rex 1650  df-v 1812  df-dif 2049  df-un 2050  df-in 2051  df-ss 2053  df-nul 2281  df-sn 2412  df-pr 2413  df-op 2416  df-uni 2504  df-br 2620  df-tr 2681  df-po 2840  df-so 2850  df-fr 2917  df-we 2934  df-ord 2951  df-lim 2953

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