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Theorem ssun4 4176
Description: Subclass law for union of classes. (Contributed by NM, 14-Aug-1994.)
Assertion
Ref Expression
ssun4 (𝐴𝐵𝐴 ⊆ (𝐶𝐵))

Proof of Theorem ssun4
StepHypRef Expression
1 ssun2 4174 . 2 𝐵 ⊆ (𝐶𝐵)
2 sstr2 3990 . 2 (𝐴𝐵 → (𝐵 ⊆ (𝐶𝐵) → 𝐴 ⊆ (𝐶𝐵)))
31, 2mpi 20 1 (𝐴𝐵𝐴 ⊆ (𝐶𝐵))
Colors of variables: wff setvar class
Syntax hints:  wi 4  cun 3947  wss 3949
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477  df-un 3954  df-in 3956  df-ss 3966
This theorem is referenced by:  ssun  4190  xpsspw  5810  uncmp  22907  volcn  25123  bnj1408  34047  bnj1452  34063  pibt2  36298  elrfi  41432  cnvrcl0  42376
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