Theorem uneq12 3652

Description: Equality theorem for union of two classes. (Contributed by NM, 29-Mar-1998.)

Assertion

Ref	Expression
uneq12

Proof of Theorem uneq12

Step	Hyp	Ref	Expression
1		uneq1 3650	. 2
2		uneq2 3651	. 2
3	1, 2	sylan9eq 2518	1

Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  u.cun 3473

This theorem is referenced by:  uneq12i  3655  uneq12d  3658  un00  3862  opthprc  5052  dmpropg  5486  unixp  5545  fntpg  5648  fnun  5692  resasplit  5760  fvun  5943  rankprb  8290  pm54.43  8402  xpscg  14955  evlseu  18185  ptuncnv  20308  sshjval  26268  diophun  30707  pwssplit4  31035  bj-2upleq  34570

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-un 3480