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Theorem intssuni2 4973
Description: Subclass relationship for intersection and union. (Contributed by NM, 29-Jul-2006.)
Assertion
Ref Expression
intssuni2 ((𝐴𝐵𝐴 ≠ ∅) → 𝐴 𝐵)

Proof of Theorem intssuni2
StepHypRef Expression
1 intssuni 4970 . 2 (𝐴 ≠ ∅ → 𝐴 𝐴)
2 uniss 4915 . 2 (𝐴𝐵 𝐴 𝐵)
31, 2sylan9ssr 3998 1 ((𝐴𝐵𝐴 ≠ ∅) → 𝐴 𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395  wne 2940  wss 3951  c0 4333   cuni 4907   cint 4946
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-ne 2941  df-ral 3062  df-rex 3071  df-v 3482  df-dif 3954  df-ss 3968  df-nul 4334  df-uni 4908  df-int 4947
This theorem is referenced by:  rintn0  5109  fival  9452  mremre  17647  submre  17648  lssintcl  20962  iundifdifd  32574  iundifdif  32575  bj-ismoored2  37109  bj-ismooredr2  37111  ismrcd1  42709
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