Theorem intssuni2 4312

Description: Subclass relationship for intersection and union. (Contributed by NM, 29-Jul-2006.)

Assertion

Ref	Expression
intssuni2

Proof of Theorem intssuni2

Step	Hyp	Ref	Expression
1		intssuni 4309	. 2
2		uniss 4270	. 2
3	1, 2	sylan9ssr 3517	1

Syntax hints:  ->wi 4  /\wa 369  =/=wne 2652  C_wss 3475  c0 3784  U.cuni 4249  |^|cint 4286

This theorem is referenced by:  rintn0  4421  fival  7892  mremre  15001  submre  15002  lssintcl  17610  iundifdifd  27429  iundifdif  27430  ismrcd1  30630

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-ne 2654  df-ral 2812  df-rex 2813  df-v 3111  df-dif 3478  df-in 3482  df-ss 3489  df-nul 3785  df-uni 4250  df-int 4287